Bigger isn't always better- a pellet that passes through an animal doesn't deliver all of its energy potential.
Remember your Saturday morning cereal bowl after you've eaten all of the cereal? The milk would be red or blue, or if your liver could process that much sugar, brown?
That's left over sugar energy. The bowl of cereal solids you did consume gave your body energy, but there is still more in the milk left at the bottom.
If you vacuum up all of that sugar sludge, you've taken out all you can. A good hp bullet, rifle or pistol driven, can transfer a high percentage of kinetic energy- a solid, non/ little expanding pellet, going all the way through an animal and then continuing in it's Merry way, is taking its energy with it.
Accuracy, with pellets, is my preferred choice, with energy second- for solid projectiles. If there a pellet that takes all of its energy and dumps it into the animal, you may be able to anchor an animal cleanly with a little less precision. Spend time watching your game's passing into the other side, adjust your aim and desired hold points (and distance), until you can get the quickest possible result.
Love hunting, been doing it for lots of years ( went out ratting last nite ) but injurying an animal, or seeing pronged suffering breaks my heart. Keep asking questions, share what you observe and we can all learn from each other.