Any of these can diagnose Autism, but they should have Autism and Behavioral Disorders included in their specialties: Pediatric Psychologist, Pediatric Psychiatrist, Pediatric Neurologist, Developmental-Behavioral Pediatrician.
If you call your local Children's Hospital and asked for "whichever department handles Autisms" they would most likely direct you to their Developmental-Behavioral Pediatric Department. We got our initial diagnosis from a Pediatric Psychiatrist. That diagnosis was agreed upon by our first Pediatric Neurologist, and again by our current one (who "tightened up and clarified" the diagnosis). Our pediatrician has been on board with all of it. The P. Neurologist also confirmed ADD and finally helped us treat it. She's been all around wonderful for us, as she's familiar with all of the issues we have to deal with and is also familiar with all of the professionals in the area that can help us (if only our insurance would stop dicking us around).
So, as to which one is best, it depends. It depends on who you find and how specialized they are Autism Disorders. They are all correct, but it's not fair to say which one is "best."