CP- you get to experience front-line work. This is very important if you want to move up within the company, the vast majority of managers start doing front-line. You also get experience assisting Guests, creating magical moments, and practicing guest recovery. Also, there is typically more advancement opportunities in front-line world. CM - Trainer - Coordinator - Manager.
PI - you get to experience backstage work. For my particular role I had a cubical in Team Disney. You will get a much larger picture of the company and discover how departments work together and all the little details I did not see during the CP. However, since most start in front-line and move to a professional job, the advancement opportunities are a little more difficult (depending on the area).
I did both programs back to back. I was offered to stay in my PI role (turned to TA) or to accept a job back in front line. Since I personally am looking to get into management, I knew there were no options in my PI area, so I took front line (and a pay cut) and returned to the park. I've already received trainer and am applying shortly to move into coordinator.
I do hope to get back into the professional world again, but since Disney lives on the front line people they typically look for those who have given their service to Disney.
Others may have completely different opinions - this is just what I ran into (based on my specific PI).