Many people of yesteryear made the mistake of shooting big mean animals with bullets designed for deer and human targets. This simply doesn't work.
As many have alreay pointed out = it's all in bullet design, bullet weight, and shot placement. I will also point out that high velocity doesn't equal dead animal. Many studies have been done that suggest that heavy, slow/moderate velocity bullets penetrate much deeper.
I agree with the above study. In my non-scientific testing my .45 Colt loaded with 300 gr hardcast at around 1100 fps will penetrate further in wet phone books than my 270 or 7mm-08. If I was shooting something hard like steel then the high velocity round would carry the day. I think it's because the higher velocity rounds shed their enegy faster on softer targets. The slower and heavier bullets just have more momentum.
Edit: I will do some more non-scientific testing with my .358 Winchester loaded with BB's 225gr. Barnes TSX loads.