I consider it both their episode.

Both Pinkie and Applejack play a central role in the episode. There is such thing as paired episodes within the series. Both characters have something to do with the important things of the episode (Applejack is trying not to ruin Pinkie’s family time with her, Big Mac, Granny Smith, and Applebloom. And Pinkie wants to know if she really is related to Applejack), they both have a strong part of the ending and/or moral in the episode. (Applejack says at the end it doesn’t matter to her whether or not Pinkie is related, her time with them during the trip has made her consider her one anyway.)

If I had to lean towards one side, I’d actually say it’s more of an AJ episode because the explicit moral has Applejack learn something more then Pinkie did. (Exact quote: “bein’ a good family isn’t about bein’ perfect as much as it is about bein’ able to get through the rough patches together. About bein’ able to forgive each other for mistakes”) but that’s not to say Pinkie wasn’t a big part of the episode.

It’s similar to Testing, Testing, 1, 2, 3 where the main point of the episode makes it seem more based on Rainbow. But there’s also quite a bit of Twilight focus in the episode as well. So in essence that episode was a Twilight & Rainbow episode. In the same way, I count Pinkie Apple Pie as both an Applejack and a Pinkie Pie episode. The episode doesn’t go the same way at all if either of the two ponies roles are diminished from where they are.