pick one that shoots well.
That's what the man said.
An animal gut shot with a 180 will suffer far more than the one shot in the lungs with a 150.
Today's bullets are vastly improved. In the days when bullets didn't hold together very well, using 180 grains going in meant 100 to 120 grains left. With some of the current bullets, you can shoot an animal with 150 grains going in, and 149.5 grains going out.
I've shot elk with a 30-06 with bullets weighing 150, 165, and 180 grain. To be honest I'd probably have a slight preference for 180 grain, but only if they shot as well and had the same ballistic characteristics as a lighter bullet.