Eileen and I have a bunch of big game rifles too, like most people here, and use both cup-and-core and "premium" bullets in them. We choose the bullet according to the game and the velocity, and haven't had any problems in many years.
Anybody who thinks a Hornady Interlock Spire Point isn't an adequate deer bullet even at 3000 fps or a little more simply hasn't tried them, and in heavier weights at sub-3000 velocities they work well on bigger game. There aren't many species of big game I'd worry about hunting with 250 Interlocks from my .358 Winchester or 286's from my 9.3x62.
in my experience Nosler Ballistic Tips work very similarly to Interlock Spire Points, whether their weight when recovered, on the rare occasions they are, or how they kill stuff.
But Eileen also loads the 180 Speer Hot-Cor flatnose at around 2000 fps in her German combination gun, which is supposedly a 9.3x72R but has a .35-caliber bore. It knocks the snot out of deer and we haven't recovered one yet.
I've also use several Sierras in various cartridges, and know from long experience that the 160 GameKing works very well on deer and similar-sized game from the 7x57 Mauser, whether in North America or Africa.
But we also use several premium bullets, which work very well in specific applications too, including Barnes TSX's, Cutting Edge Raptors, Nosler Accubonds, E-Tips and Partitions, and others. Might even call Bergers premium bullets, because they act a little differently than the others listed above.
Hard to go wrong with any of today's bullets if they're used with some understanding of the ways various bullets work and can be applied. Which is why its often amusing to read very firm opinion about how one bullet or another is the absolute answer for every kind of big game hunting.
