The only pets I've ever had other than dogs is mice. So I can only really comment on dogs.
I own bully breeds exclusively, and 90% of those are pit bulls. We have adopted an adult pit bull twice. Both were great dogs, with 1 shared flaw. They both were extremely toy and food aggressive. Most behavioral issues can be fixed in adult dogs. If you adopt a dog that doesn't walk on a leash the right way, for the most part the worse that can happen is you'll end the walk with a sore arm. There are a lot of much worse things that can happen when you are dealing with a breed that was historically bred to be aggressive towards other dogs, and giving it an excuse to be aggressive.
We had one fight break out over an apple. They each had one, our female decided if she took our males, then she would have 2. They were wagging their tails about it, nobody was growling or acting aggressive, so I made the mistake of getting my camera instead of fixing it. He decided he wanted his apple back, and before I could turn around with the camera she attacked him. This was completely my fault, I should have corrected it in the first place, but if I had gotten her as a puppy and taught her at a young age that toy and food aggression isn't ok, it might not have happened.
For that reason alone, if we have multiple dogs, which we always do, I prefer my pit bulls as puppies.