I am super busy at work right now, but I started a post with my opinion on the conflict. Here's what I've got so far, although it is a work in progress and I will add to this significantly as soon as I have the time:
This is a very interesting (and might I say epic) conflict that probably really happened from time to time in the Miocene. There are many factors which come in play, most of which are speculative to a degree, but for which we can make some fairly reasonable inferences.
First, as Grey has pointed out, it may be that Megalodon had a significantly larger bite in terms of volume than Livyatan. This seems to be case when viewing the jaw constructions. Megalodon has a far wider and higher "circular-shaped" bite, while Livyatan's bite is long and relatively narrow. It's still an enormous bite, but probably quite a bit smaller than a full grown Megalodon.
However, I offer this caveat. It may very well be that a large great white has a larger bite volume than an orca. Just comparing orca skulls to large great white shark jaws leads me believe that an orca's bite, while powerful, is not extremely voluminous compared to a large great white. Indeed, if all one had to compare the two animals was a large great white shark jaws vs. an orca skull, one might conclude that the shark was the larger animal. Yet we know that is not the case and that orcas in fact substantially outsize even the largest great white. Moreover, we know primarily because of that size difference, orcas generally will dominate great whites.
Now I do not make that statement to suggest that Livyatan was necessarily larger than Megalodon - in fact I think it more likely that the shark was larger. However, just as with orcas v. great whites, we can't simply assume that the larger biter between Megalodon and Livyatan is declared the automatic winner. Bite volume is an important factor, but it is one of many.
Next, is the question of which animal had the deadlier predatory bite. I would divide this into three general categories, (1) bite force (2) bite damage, and (3) bite volume. I believe Megalodon probably holds the advantage in at least two of these areas, but is probably very close overall. First, and easiest to determine is bite volume. As already explained above, it is likely that Megalodon had a significantly larger bite, which means in theory it could remove more flesh and/or attack a larger surface area on the body of prey/competitor than Livyatan could. This is a significant advantage since it means that Megalodon likely could remove more flesh and cause more internal injuries in a single attack than Livyatan could.
Bite volume is closely related to bite damage, but damage includes not just the volume but how the teeth are doing their damage. Megalodon's teeth are broad, thick, dagger-edged and serrated. Livyatan's teeth are massive, conical, smooth, and sharply pointed. Megalodon's teeth are perfect for slicing through flesh and even bone and also are massive and thick enough to permit some crushing ability. Livyatan's teeth are designed for holding and crushing, but they clearly also have the ability to pierce and slice flesh and bone. Both sets of teeth are pinnacles in predatory apparatus, but for the overall bite volume and ability to saw off massive amounts of flesh quickly, I give Megalodon's serrated teeth the edge in "deadliness."
As for bite force, it is unknown for each of these animals although Megalodon's bite force has been estimated at 20 tons or more for its maximum proposed size. Given the thick skull structure of Livyatan, its tooth structure, and the room for massive mandible muscles, we can assume that Livyatan's bite force was also very great. We have no known orca or other cetacean bite force to use as an analogue, but it is not an unreasonable assumption to think that it may have had an even greater bite force than Megalodon. So as far as bite goes, I believe Megalodon probably had the overall most deadly bite, but both animals' bites were incredibly formidable. We should also include lateral shaking as helping Megalodon generate perhaps even a greater bite force, since a wide variety of sharks exhibit this behavior. However, orcas have also been observed to employ lateral shaking in their attacks on whales, and Livyatan may have incorporated such behavior as well. It is a logical feeding/attack behavior for a superpredatory marine animal. So we cannot exclude Livyatan from the extra bite force generated from lateral shaking.
But beyond the respective weaponry, there are many other biological and behavioral factors which must be considered. Of course, sheer size is a factor. The Livyatan holotype is estimated at 13.5 to 17.5 meters. A large bull sperm whale may weigh 50-60 tons, so this is probably a good rough estimate for Livyatan at the upper size range. A 13 meter Livyatan may have "only" weighed around 30 tons.
Megalodon has been estimated at 50 to over 100 tons. It probably weighted somewhere between those numbers but IÂ’d be surprised if it reached maximum hypothetical weight. Determining size based on tooth analysis warrants its own thread, but it is safe to say that Megalodon adults may have ranged from 15 meters to over 20 meters. As I've said many times before, there is unpublished evidence that, when it comes out, may support the idea of Megalodon reaching the upper length limit. However, I will not rely on that until it is officially published. In general, I think the size range of Megalodon is a bit larger than Livyatan's, although I know some members like coherentsheaf have made some good points in the past taking issue with how Megalodon's size is currently extrapolated.
There are other factors which must come into play. Which animal was faster? Which animal was more maneuverable and which had more stamina? Here, I think there are some plausible arguments in favor of Livyatan. Both these animals were behemoths. Yet we see that large whales like sperm whale (closest analogue to Livyatan) can be relatively fast, obtaining top speeds of over 18 mph (30 kph).
See
marinebio.org/species.asp?id=190. One could reasonably assume that Livyatan, as a presumably more active and formidable predator than the suction feeding sperm whale, would be able to attain similar or even faster speeds. Moreover, sperm whales, like most cetaceans are known to be able to maintain high speeds for a long period of time, suggesting relatively high endurance.
Megalodon's top speed is even more mysterious. Using the modern day analogue (but much smaller) great white, adults can probably reach or exceed 25 mph in predatory attacks. Some researchers even think it may be able to obtain 35 mph in bursts. See, e.g,
ocean.si.edu/great-white-shark; www.sharkinformation.org/great-white-shark/. Moreover great whites are known to have great endurance in some respects. They sometimes pull fishing boats for hours and many miles out to sea.
However, using a great white as an analogue for these behaviors is problematic. Although most researchers believe Megalodon belongs with the great white in the lamnid family, some researchers such as Mike Ward postulate that Megalodon may have been more closely related to sand tiger shark family (although in private communications he admits this is more a hunch and has less “scientific basis” than the lamnid proponents like Drs. Gottfried and Kent).
[Will add more when I have the time].
