In my view, behaviorists are more about resolving emotional/psychological issues your dog is having while trainers are more about teaching your dog a certain behavior.
Take my Cat-dog. She is afraid of other dogs.
A behaviorist is a better choice because they are focusing on teaching her not to be afraid of other dogs, whereas a trainer is focused on getting her to walk past another dog without a reaction. The first works to resolve Cat-dog's fear, the second simply focuses on the end result (my being able to walk her around other dogs).
If your dog is simply pulling while walking, then a trainer is sufficient. If your dog is pulling because she wants to run away from scary things, then a behaviorist will be more effective in the long run.
As for aversive methods, that doesn't differentiate between a behaviorist and a trainer. There are both that use aversive methods and both that use non-aversive methods.
For pulling, check out kikopup videos on youtube. They use non-aversive methods to stop a dog from pulling.
My logic is that if I can train my dog without resulting to punishment, pain, etc, then I owe it to my dog to do so.