The weight of the bullet has less to do with the outcome than the construction of the bullet, and all bullets are a compromise. If you knew ahead of time what range you were going to shoot, you'd pick the right bullet. It just don't work that way, though.
As the target gets farther and farther away, the velocity drops off, and a really tough bullet like a Barnes X won't expand, since it's really intended to penetrate heavy animals and also to not fragment in a close-range high-velocity hit. A softer bullet (ideal for a long-range shot, because it will expand at lower velocity) is exactly the wrong thing for the deer that suddenly appears 25 yards away. Remember... you DO want the bullet to expand and not exit; that way, it expends all its energy on (in) the target. If not, it will just drill right through the animal and, unless the lungs or heart are hit, you have a lot of trailing in your future, and a small exit wound (small blood trail).
What all the premium bullets are trying to do is retain a fair amount of weight in a close hit and be able to penetrate on a heavy animal, yet still expand, at least somewhat, at longer ranges/lower velocities. The Swift A-Frame, Nosler Partition, and Barnes X are probably the best known of the bunch.
Anything with "bonded" in the title is also designed to keep the jacket and core from separating, thereby giving a higher retained weight percentage and better penetration, yet still having a soft enough nose to expand at lower velocity.
If you figure on shooting whitetails at reasonably close range (100 yards or less), you should take up handloading and look into reduced loads for the .300 Wby.