Like anything else, "It depends"...
I try to choose a bullet based on what I'm hunting. If I would normally be satisfied with a 'standard construction' bullet, I'll likely use the same thing even if going 'heavy for caliber'.
If I would normally be using a 'tough' bullet for the intended game animal, then the heavy bullet will likely be 'tough', as well.
Generally speaking, though, if I think I need to go 'tough' and the standard bullet weights for the cartridge seem inadequate, I'll be looking to increase the size of the hole, too.
If I think my normal .243 Win loads aren't appropriate, I'll be looking to the .270 Win or .30-06. If I think they are inadequate, then the .35 Whelen or a .444 Marlin might be the go-to. And if they still don't seem big enough, I can stuff some 430(+) gr bullets in the .475 Tremor or .480 Ruger. There's a velocity penalty, but they hit hard, penetrate well, and make big holes.