I will say that an animal being hit hard & the way it reacts can be very specific to the individual animal. Boddington (& others) have stated that they have seen buffalo hit broadside, in the shoulder, & drop from a 375-class cartridge (not often though). He then states he has seen buffalo hit in the same spot w/ a 416-class & run 100yds. Some individual animals are just more tenacious & determined than others. This being said, any advantage in frontal area, sectional density, & energy definitely helps, but the difference may not be as much as the difference of the individual animal.
As far as classic goes: I like the 404J. I get that it is more rare & debuted 7 years earlier, BUT IMO the 375 H&H is equally as classic. There also may be a reason the H&H isn't as rare...components, rifle platforms, etc.
As far as bullet weight/velocity goes: I agree with pretty much all on heavy for caliber & moderate velocity (this is also more classic too). Where I deviate from this is when Barnes X bullets enter the equation, because a TSX will not fail from being pushed too fast. Barnes TSX love velocity & they will penetrate deeper the faster they are pushed. In terms of terminal performance, bullet construction is far more important than cartridge selection (within the same reasonable class).
You could not go wrong with either of these cartridges, but the 404J does get the nod on buffalo-range killing power.
The decision between THESE two should not be focused on killing power, but on personal preferences. If you really want to step up the killing power jump to the .458-class.