I haven't really seen any trends in adoptables/sim sites. They're pretty much stayed the same since the old childhood days of Neopets; which is how a lot of adoptables/sim sites got started, trying to mimick the neopets formula. Not that that's bad, mind you. It opened up to more creative ideas and concepts. I remember Foopets which was a 3D adoptables site, before it eventually became paid-membership only.
I noticed a couple of games that focus on realistic/semi-realistic genetics more recently, like Leporidae and Dynasty, but I don't think there have been enough for it to be called a "trend".
I've also noticed that a few adoptables/sim sites have a more semi-real/realistic style than the cartoony style that appeared to be a staple for pet sites. But again, I haven't seen enough of these sites for it to be a trend and it's possible that those sites have always existed, but I just didn't know about them (I know Howrse has been around for a long while), plus those cartoony sites tend to be geared towards children.