I'm quite sure that light-for-calibre monometals are quite deadly, even on big game. Just last year (or the year before) the regulations changed here, so that the minimum for big game (i.e. moose, bear, red deer, boars etc) is a 120gn bullet at such a speed that it energy-wise matches the previous energy minimum (e100) for lead-core bullets (which had to be 155gn or more).
Sure, they have the same impact energy, but won't have the same momentum. Partly I believe this is a slightly "political" thing - as a) politicians want to make a statement on lead (even though metallic lead is not the same as leaded gasoline), and b) the 6.5x55 Swedish is still one of the main calibres here, and there is a physical limit on chamber pressures/bullet weight/energies etc that are realistic/safe. And no politician (at least from parties that count) want to make enemies with the hunting community by effectively "banning" 25% of all rifles from big-game hunting.
So far I have almost only heard positive reports on the use of monometals (in any calibre) locally. But I do suspect that a lot of people still want to use leaded bullets for hunting situations where you a) don't want pass-throughs/ricochets. We often hunt with dogs, and also when the ground is frozen. Thus, a hard projectile can increase the risks of injury to 'bystanders'.
Therefore I personally prefer bonded lead core bullets like the Norma Oryx, North Fork PP or similar, as if the bullet exits, it will have less capability to unintended damage.