Well after a lot of difficulty, I was finally able to ask another question. I think you gotta change this 1 question per day system. Anyways let's go!
1. Chacma baboon vs Olive baboon
2. African hunting dog vs Thylacine
3. I once saw on TV, a lone male jackal fight off 2 ratels while he was guarding his pups. This led me to the belief that a gray wolf can defeat a wolverine if forced to fight a long drawn battle. So,
Ratel vs Black backed jackal
4. Gray wolf vs Wolverine
5. African hunting dog vs Wolverine
6. African hunting dog vs Chacma baboon
7. Chimpanzee vs Bully Kutta
8. Thylacine vs Olive baboon
9. Javan Rhino vs Spanish fighting bull
10. Siberian tiger vs American black bear
11. Guar vs Dinohyus
12. Salwater croc vs Leopard seal
13. Epicyon vs Marsupial lion
14. Epicyon vs Hyenodon
15. Do you have any idea about the biting power of Dinohyus?
16. Caracal vs Arabian wolf
17. Caracal vs Ratel
18. Caracal vs African civet
19. Deinosuchus vs Liopleurodon
20. Leopard vs Sloth bear
21. Short faced bear vs Helloid
22. Olive baboon vs Gray wolf
23. Cougar vs Silverback Gorilla
24. Cougar vs Sloth bear
25. Main event: Snow leopard vs Chimpanzee
1. Chacma baboon vs Olive baboon: The chacma baboon typically gets heavier, but not by much. The olive baboon has a a relatively stocky build, but the Chacma's build is comparable. At equal weights I would favor the olive, but the chacma has a large enough size difference to swing the contest in its favor. Edge to chacma baboon.
2. African hunting dog vs Thylacine: The African wild dog is slightly heavier than the thylacine, and has a stronger set of jaws. African wild dogs are practiced predators of large game, and occasionally scuffle with a variety of African predators. They are built more robustly overall than the Thylacine as well. Reasonably close fight, but the African wild dog wins.
3. Ratel vs Black-backed jackal: These animals will weigh about the same. The ratel (or honey badger) has a reputation for being fearless, and its thick skin, sharp claws, & strong jaws give it reason to be. Black-backed jackals are quick & bold, but their bites are their only weapons. Although they have gotten the better of ratels from time-to-time in certain situations, a full-fledged battle between a ratel and a jackal will definitely favor the ratel. Ratel wins.
4. Gray wolf vs Wolverine: A gray wolf can weigh as much as 3 wolverines. The wolf's only weapon is its bite, but it's a big one, and the wolf has the lateral movement to employ it effectively against the stockier mustelid. Wolverines have sharp claws on their powerful limbs, and their jaws can crunch through frozen meat & bones. As ferocious as the wolverine can be, it is seriously outweighed here against a very capable predatory combatant. Not an easy contest for the wolf, but it should have the size & bite to eventually pull this off. Gray wolf wins.
5. African hunting dog vs Wolverine: The African hunting dog will have a 70% weight advantage over the wolverine. The wolverine is a very strong animal pound-for-pound, and can be bold & aggressive. The mustelid has thick fur, sharp claws, & a bone-crushing bite. The African wild dog is nimble, and has a strong bite force of its own, but it typically takes on other animals in a group. In a realistic situation the wolverine would likely succeed in driving the wild dog away, but a persistent one could make a good fight of it. The wolverine has a more robust & supple body than the canid, and it has a greater variety of weapons at its disposal. Close battle, but the wolverine has the slightest of edges. Wolverine wins.
6. African hunting dog vs Chacma baboon: A large chacma baboon can weigh 20& more than the African hunting dog, and will use its mobility, hands, and sharp canines to attack the wild dog and inflict quick injuries. The African wild dog is nimble & persistent, and has a strong bite force. Both combatants will receive injuries, but the baboon will dish out the more serious ones. Chacma baboon wins.
7. Chimpanzee vs Bully Kutta: The Bully Kutta will weigh about 30% more than the chimpanzee. Bully Kuttas have thick bones & muscular bodies. These agile dogs have been used for guarding, protecting, & fighting. A chimpanzee might succeed in deterring a pet Bully Kutta from advancing upon in with an intimidating display, but a trained Bully Kutta will attack readily. The jaws of the canine will be hard for the chimpanzee to avoid (even with its grabbing hands & strength), and its own bite will not have the same kind of effect as the Bully Kutta's. The dog will have a better chance to finish the ape than the other way around. The larger Bully Kutta wins.
8. Thylacine vs Olive baboon: The thylacine weighed about 85% of the baboon's weight. Thylacines were lightly-built marsupials with wide-opening jaws. The baboon would have enough mobility to employ its dangerous bite effectively, and the bite of the thylacine wouldn't have been enough to combat this. Olive baboon wins.
9. Javan Rhino vs Spanish fighting bull: A Javan rhino can weigh almost twice as much as a Spanish fighting bull. Its thicker legs & tank-like build would enable it to bully the smaller bovid into retreat, and could use its horn to plow into the bull if it stood its ground. The Spanish fighting bull is a very aggressive animal that is packed with muscle & armed with sharp, forward-pointing horns, but it will be overpowered by the larger rhino. Javan rhinoceros wins.
10. Siberian tiger vs American black bear: These animals will weigh about the same. The Siberian tiger will be quicker, more agile, and have better killing experience than the black bear. The black bear will have more brute strength & endurance. The tiger will have the agility to eventually obtain a favorable position to land a finishing neck bite, but it won't be easy. The black bear will have strong paw swipes that can do damage, but they won't be as quick as the tiger's paw swipes. It's a reasonably close fight, and a long battle will slowly shift the advantage to the bear, but the tiger should have the predatory instincts & skill to defeat the bear more times than not. Siberian tiger wins.
11. Gaur vs Dinohyus: This will be a close fight. The gaur can get somewhat heavier. but the bite & tusks of the Dinohyus might actually be better weaponry than that of the gaur. The gaur is very muscular & powerful, and has large, curved horns. I would favor Dinohyus at parity, but a gaur with any weight advantage over 20-30% would probably have the edge.
12. Saltwater crocodile vs Leopard seal: The saltwater crocodile will weigh almost as much as 3 leopard seals. Leopard seals are active predators, and have jaws armed with 1" canine teeth. They move through the water with ease. Crocodiles are covered largely in osteoderms (bony growths), and have vice-like jaws and a powerful tail. On land or in shallow water, the crocodile would be favored due to its large size, jaws, & the limited mobility of the seal. Once in deep water, the leopard seal would have a decided mobility advantage over the saltie. However, the seal would find it hard to exploit this advantage because its teeth wouldn't easily penetrate the crocodile's tough skin. The crocodile's ability to make quick movements with its head would give it a chance to clamp onto the seal as the mammal attempted to land multiple bites. It might take a while, but the crocodile would get the upper hand at some point. Saltwater crocodile wins.
13. Epicyon vs Marsupial lion: Epicyon haydeni, the largest of the Epicyons, weighed a little more than the Marsupial lion. Epicyon had powerful jaws, but the Marsupial lion's bite force was even more so. The Marsupial lion also had a more robust build, and was accustomed to conquering large prey items. Marsupial lion wins.
14. Epicyon vs Hyaenodon: The largest species of Hyaenodon was the Hyaenodon gigas, which was over twice the size of Epicyon haydeni. Both animals had big bites, but size matters with this one. At parity I would call it close to a draw, but at these weights the Hyaenodon is too much. Hyaenodon wins.
15. Biting power of Dinohyus: Bite force isn't my forte, but Dinohyus had had powerful neck muscles and large canine teeth that indicated a bite that could break bones. Its head alone was almost a meter in length, and its width was enough to allow room for large jaw-closing muscles.
16. Caracal vs Arabian wolf: The caracal can get slightly larger than the wolf. The caracal will be quicker, and has the advantage of claws. The wolf's only real weapon is its bite. The wolf will try to land many bites (or grab onto the neck area & hold), but the claws of the caracal will swiftly slash at the wolf in defense. Close fight, but the caracal has the edge.
17. Caracal vs Ratel: The caracal can weigh up to 40% more than the ratel. The ratel has thick skin that will protect it from a lot of the caracal's offense (claws & bite), and the ratel's offense (also claws & bite) will be sporadic against the quicker feline. Durability will be the ratel's biggest advantage, and quickness will be the caracal's biggest advantage. At parity I would side with the ratel, but at these weights its closer to a 50/50.
18. Caracal vs African civet: The caracal will be slightly heavier than the civet. African civets have strong bites, but their limbs are not as long as the caracal's. The caracal's reach advantage with its swiping claws and more predatory nature will give it the edge in this contest. Caracal wins.
19. Deinosuchus vs Liopleurodon: This depends on the weight assigned to Liopleurodon. I've seen estimates range from 5 tons to 100 tons, but 25-50 is probably more reasonable. Deinosuchus was a huge alligator-like creature that was twice as long as modern crocodiles and 8 times as heavy. The Liopleurodon used 4 long flippers to navigate through the water with great agility (and was capable of quick bursts of speed). Both of these animals had formidable jaws. At equal weights I would favor Liopleurodon in open water, but in shallower water where the pliosaur's mobility would be compromised, I would give the edge to Deinosuchus. In open water I would favor a smaller Liopleurodon to outmaneuver & defeat Deinosuchus, but only if it was at least 75% of its weight.
20. Leopard vs Sloth bear: A sloth bear can be double the weight of a leopard. Sloth bears can be aggressive, and have long (3") foreclaws that can cause serious injury to an attacker. Leopards are powerful & well-armed (jaws & claws), but they aren't going to have a great showing against a bear of this size. Sloth bear wins.
21. Short-faced bear vs Helloid: The short-faced bear will weigh about 4 times the Helloid's weight. The Helloid is ferocious, and has long claws & teeth, but it will be overpowered by the much larger bear. Short-faced bear wins.
22. Olive baboon vs Gray wolf: The Olive baboon will weigh a little more than 60% of the wolf's weight. Olive baboons are solidly built, and have sharp upper canines that can cause quick, deep wounds to an opponent. Wolves have good stamina, and large jaws with decent bite force. The wolf will be able to latch onto the baboon rather quickly with its jaws (although it will likely receive a few bites in the process), and try to finish by shaking or releasing to bite again. It's a dangerous battle for the wolf, but the baboon won't have an answer for the canid's big bite. Close fight, but edge to the gray wolf.
23. Cougar vs Silverback Gorilla: The cougar will weigh about half of the gorilla's weight. Cougars have agility, jaws & claws, & excellent predation ability, but a silverback gorilla might be just out of its range. The clubbing forearms, grabbing hands, & strong bite of the ape will probably be enough to send the smaller felid packing. The cougar can win, but the brute strength of the gorilla will enable it to dictate the actions of this encounter more times than not. Silverback gorilla wins.
24. Cougar vs Sloth bear: The cougar will weigh about 55% of the sloth bear's weight. This will be similar to the leopard vs sloth bear result, with the bigger bear being a bit too much for the cat. Cougars have been known to drive away larger bears in their habitats, but driving away & fighting are 2 different things. Sloth bear wins.
25. Main event: Snow leopard vs Chimpanzee: These animals will be similar in weight. Chimpanzees are strong, and they can be hostile, but they don't have experience (or predatory know-how) in dispatching similar-sized animals of another species. Chimps have turf wars with baboons from time-to-time, but they usually resort to intimidation and boisterous displays when confrontations occur. Apes don't deal well with similar-sized cats. They don't have an answer for the agility, explosiveness, & weaponry a big cat brings to the table. A snow leopard is a practiced hunter, and can subdue animals 3 times its on weight. It would easily claw & bite a chimpanzee during an encounter, and the chimp's options to counter this would be limited. A big chimpanzee might have a chance against an much smaller snow leopard, but not a typical one. Snow leopard wins.