I voted thrice because I am a cheater ;)
In all seriousness, the main question of this thread was a little vague, so I decided to come up with three definitions of "favorite" and pick them in those selected categories. Fidgit would be my favorite CAP overall; it fit its concept nicely, it wasn't terribly broken at its time, and it is absolutely adorable. Despite CAP being in its younger stages at the time, I get the impression that things went well when I read its process threads.
I chose Arghonaut because it is my favorite Pokemon flavor-wise. Aragonbird's artwork is gorgeous and I think it's the most "Pokemon"-looking CAP we've ever created. The movepool matches its boisterous tone and it's a scream to see it play out live in Battle CAPacity. Although its concept was critiqued heavily at its time, I really liked the idea of a Decentralizer, which went on to be the basis of my CAP3 Concept Submission. Also, its pre-evolution is adorable.
Lastly, I voted for Necturna because it is my favorite process that I have actively participated in. I was so skeptical when I saw that we were giving CAP2 Sketch; I refused to believe that we could make something that wasn't broken. The playtest blew me away: Necturna wasn't broken in the slightest. It could dutifully run a myriad of sets well, but none of them broken the Pokemon. It has some solid checks and some good counters once you discover the set. Overall, I think it is a Pokemon that played out very elegantly during the playtest thanks to our careful planning and attention to limitations of power.