My dog catches birds 3-4 times every season. Generally they are hens...not too often a rooster holds tight enough to get caught. If they aren't dead, they are generally pretty well crippled. If that's the case, I put them out of their misery.
There have only been a few times I've been able to release them to live another day.
I always - ALWAYS - leave them in the field. It kills me, but I'm not willing to risk the consequences.