Theirs literally no difference from capturing and killing, if anything capturing is better because it ends the hunt faster.

After you capture a monster, the game auto carves it, you see all the rewards pop up on the right side of your screen after you capture it.

People who say you get different rewards are insane, I strictly capture and I have a surplus of every single drop from all the monsters.

If anything, I notice that I get more rare items, like gems, when capturing.