I keep one of each.

If I happen to trap a rare of something I had a lesser quality version of, I release the lesser quality pet.

I have no need of them, they clutter up my journal, and they're probably happier off in the wild anyway.

I picked up a rare crimson the first day I could see them after maybe 20 minutes of autocancelling fights without rares. Maybe I was lucky. I have NOT seen a rare green or yellow one of any quality, though, so I guess that was the trade off? I wasn't sure if this pet would be in my thinger, cause so...