It depends...
Hey Glamdring, Good question which each hunter would do well to consider "before" going afield.
I prefer Exits on all my Game too. Definitely doubles the chance of having a blood trail. But, I'd suggest that you would do well to think of one specific Game animal, the terrain where it will be hunted and your ability to place that bullet into just a couple of spots on that animal. Then pick a bullet based on those requirements. Each of them can cause the answer to your question to be slightly different and still be correct or totally wrong.
For example, a larger diameter bullet "typically" makes a "larger" Exit, but not always. The confusing part is that it depends upon the bullet design envelope. Some bullets are designed to maintain a "smaller" diameter (after expansion) than others. A FailSafe or a Partition come to mind as doing just that. Their ability to maintain a good portion of their initial weight coupled with the small expanded front keeps the Sectional Density high thereby ensuring good deep penetration, but creating typically a smaller Exit.
The opposite of that would be any of the "Tipped" (synthetic or brass) or "Hollow Point" bullets which by design open to a very wide front, and even if they retain a good portion of their weight, the effective Sectional Density is reduced, so the bullets ability to penetrate is also reduced and may not Exit at all.
Depending on what Game the hunter is after, one type of bullet is just better than the other. And, in most cases, there are good old, Standard Grade bullets which will work to perfection. But, in some situations, a Premium bullet will certainly work better. Here is where gleaning the knowledge from experienced hunters, that have hunted specific terrain, with specific calibers, at specific distances and specific Points of Impact on that Game, can be invaluable information. "BUT", for the information to be useful, you need all the details you can pry out of that more experienced hunter to help you make the right choice for "your" situation.
Shot location is critical. It is much better to hit in the "lower-and-forward" 1/4 - 1/3 of the animal. Picture a large-wide telephone dial pad imposed on the side of a Whitetail, standing broadside and facing to your left. Here #7 would be the "key" spot to focus on.
This is because when the animal is hit "high", the blood often begins filling the body cavity prior to reaching a level where a significant amount of it can be "blown out". So, the "lower" the Exit is, the better the chance is of a useful amount of blood coming out.
Also, if the Exit is too far back, the guts can shift around as the animal moves and effectively "Plug the Exit" resulting in no blood trail. So, having the bullet path through the Game "forward" of the guts is a significant advantage.
I hope this did not end up confusing the thought process for you. Just remember when a person recommends something that it worked for him under a specific set of circumstances and you need to know as many of the specific factors as possible.
Good hunting and clean kills, Hot Core