I like them all, but I think cats are implemented the best. They're cute, fun to watch and I don't feel bad leaving a cat to its own devices for a while. With a dog and especially with a horse, I get a lot more twitchy when I see the pet running all over town because "realistically" speaking that spells trouble. If you want to avoid that, you need big (locked) pastures to keep a horse happy, and even then its mood can plummet quickly if its pathing bugs when trying to "gallop around" or play with the horseball. The need for space isn't actually a bad thing though, because it's very realistic. Locking horses into a stall is definitely a terrible way to keep them, and I'm rather glad the game reflects that through the exercise need.
What bugs me about dogs is that many of the premades look so utterly weird, more like a caricature of their breed than an actual member of it. Horses also suffer from that to a degree, you can get some really weird-looking anatomy on them (on top of the equally weird way the game handles color inheritance).
Dogs have a couple more interaction options than kitties.
In terms of money-making "best", I'm sure horses have the most potential: a daily competition or two, plus income from stud fees and from selling. On the other hand, this does require a Sim's active involvement while a dog or cat can just go hunt alone anytime and anywhere to add a small trickle of income to the family. If you're lucky, you can actually make more money that way than with a newly-employed Sim.
