I`m know little about ammo and their ballistics.
Question: If you have a 40 grain bullet traveling at 1200 ft. and you compare it to a bullet that is traveling at 1/2 the speed 600 ft. and the bullet is 2 times heavier 80 grains. Which will have the greatest impact on live animals?
Is diameter of the bullet any more important than the speed or vice versa?
As other people have pointed out, the most important factor with any shot taken on an animal is the shot's placement. A 30-30 might be an outdated piece of technology from over 100 years ago, but there is a reason it still is being used today - it does its job. You just have to be sure to do yours.
What follows after that is kind of tricky to explain. Others have already brought up the the concept of hydrostatic shock. This is the effect the transference of energy from a bullet has on the flesh of the target. Flesh is made to move and be malleable, it's advantageous for it to be so to help avoid injuries and the such. When enough hydrostatic shock occurs, it moves the flesh beyond what it's meant to. This is what can cause such horrible damage, especially to vital organs. While hydrostatic shock is nice and all, it's actually more important to hit and pierce those vital organs to ensure a kill. (It won't guarantee a faster kill, mind you, but a shot to the heart is a shot to the heart.) I know people will disagree with this statement, and even I do to a certain extent (after all there is a reason we don't hunt with full-metal jackets,) but I've seen shots taken with high-velocity rounds that didn't have the proper momentum for deep penetration. They still manage to kill the deer, but what would have been a quick-kill heart shot end up being a liquefied lung and a jaunt for tracking. A lot of bruised and damaged meat as well.
Momentum is key word in all of this. While we do want penetration, we want a proper amount, and not too much of it. Too much momentum means not enough energy is going to be transferred into the target as the projectile passes clean through it. While mass and velocity figure into momentum, when we're talking about penetration we rely mostly on mass. All things equal, a light projectile going fast and having the same
force as a heavy projective going slow isn't going to penetrate as much. This is because the heavy projectile has more momentum. On the flip side of the token, with the light projectile not penetrating as deeply, that means it's transferring more of its energy quicker - this is when lighter projectiles cause hydrostatic shock in flesh.
Thankfully, though, choices in bullet construction aids us in being able to have the ballistics we want with the penetration we need. Eb1 provided us with a good example of this.
All this said, though, use what you're most comfortable with, just don't go to either extreme.