To me, Uzuki is the protagonist, the main character. Rin is, more or less, the mascot of Cinderella Girls.
There was a similar duo in AKB0048
, with Nagisa (CV: Karen Iwata) being the main heroine and Chieri (CV: Mayu Watanabe) her rival. Not to spoil too much, the creators (Director: Shoji Kawamori) applied a finely crafted Solomon solution to the finale, so it's arguable who "won". Chieri was obviously more capable and received the capability prize, while Uzu.., er... Nagisa received the "heart" prize. This sort of resolution was uncommon in the anime before and perhaps we will see a replay.