I don't know that I have sufficient experience to hold a strong opinion, but my personal view is you should take the largest caliber you can shoot accurately, and use the heaviest quality solids available. I wouldn't use a Barnes TSX; if I were taking Barnes bullets, I'd use their banded solids.
My elephant no. 1 was a head-on shot with a 458 Lott/500 grain federal sledgehammer solid. I thought I'd brained it, but in fact had only stunned it. It staggered as if it was going to fall, but then started to run at a very rapid pace. At that point I was (as I later confessed to my ph) slinging bullets at anything that looked gray. Fortunately, that strategy was successful five shots later, and we didn't lose it. Elephant no. 2 was a tuskless cow that charged us down a narrow trail, so the only shot available was a frontal shot (which happily worked perfectly). Elephant no. 3 was another tuskless cow with a single side brain shot, as its heart/lung area was concealed by brush.
In each case, my personal plan had been to take a heart shot. In all three instances, my plan was irrelevant due to circumstances on the ground. So, I think you need to be ready for any situation that might arise. And to me, being ready means (to be repetitive) to take along as much gun as you can shoot.
I've actually carried my "bigger caliber" advise over even to plains game hunting. Not that a .30 bullet isn't perfectly adequate for plains game, but the last time I left the heavy artillery at home thinking there was no dangerous game in the area, we got chased by a rhino. And while we were skittering away, I was thinking constantly that a .308 was just going to piss it off, if it came down to an Alamo-style last stand. And on an earlier occasion I was sitting in a leopard blind when a baby elephant started sniffing around the blind, panicked when it smelled us, and its mother came round to see what was going on. Nothing dramatic happened there but, again, I was sweating like a fountain and looking at my puny rifle, realizing it wouldn't do much good if mama elephant decided to disassemble our blind (and us). So now, my usual plains game rifle is a .416 --- or Ruger No. 1 .450/400 when I'm shooting iron sights.