I received my Private and CFII licenses from a local FBO and from the same instructor. I happened to get lucky because I was good friends with the guy. I actually was his first private student and first CFII student as well. I hear alot of stories where peoples instructor would just up and leave when they got sufficient flight time. You gotta really look into the type of instructor you want and make sure that he'll be around for the duration of your training. It's not mandatory that you have the same instructor but it makes it nice....instead of having to find a new one half way through your training. Hope that helps ya!
I agree. It all depends on what type of training atmosphere you enjoy. I found that the FBO "Freelance Instructor" training is much more layed back. It's fun to just hang out around the airport and BS with all the older guys. You can learn quite a bit just from that alone!