As was said, you need to decide what you are comfortable with. My personal opinion is I would have done the same you did in the first instance, and put a suffering animal out of it's misery. If the other animal isn't wounded, then it's arguably not suffering. However, the odds of it surviving are essentially zero. Some predator like a cat will most likely get it. If that happens, then again my opinion is... so be it. Cats need food, and the chick wasn't going to survive outside of the next as less than a fledgling anyway. The bird that you euthanized will become food for other creatures, such as ants and other "recyclers". And with that the circle starts all over again.