Finn made me smile and root for him every time I saw him on screen. He was awkward at times (hey, not much social interaction since he was a ST from early childhood), but his heart was always in the right place. I smile when I think of his character, and look forward to seeing him in the next part of the story, EVEN if he's not a Jedi.
Jar-Jar makes me cringe when I hear him or look at him move. (That's saying a lot considering how bad the writing was for Anakin, IMO.) Jar Jar's purpose seemed to be the Comic Relief, whereas Finn has a much bigger and better-integrated role.