I don't like that I can't nickname them. :( That's the only thing that really concerns me with traded Pokémon, and even then when I'm getting Pokémon from friends, I almost always insist they nickname them because it adds something special and reminds me that a friend gave it to me.
The stat boost is nice but I don't like them to get ahead of the rest of my team (I train evenly) and the disobedience... has never kicked in since I first played Pokémon Red so I think it's kind of a moot point for me. :P
I guess all in all, these days I'd rather get eggs than a hatched Pokémon. I'd rather have full control over a Pokémon, its growth, its nickname, etc.