Fall Weather Friends (S1)
This was easy to pick for a simple reason: The two Brawns of the Mane 6 competing to see who’s the better athlete, only to have their competitiveness causing them to finish in last place. Not much else to say.
Other Nominees: Over a Barrel (S1), Castle-Mania (S4),

Pinkie Apple Pie (S4)/Hearthbreakers (S5)
For a short while, I’d considered Season 4’s Pinkie Apple Pie to be a Pinkie Pie and Applejack-focused episode, but after see Season 5’s Hearthbreakers, I believe the latter is better. In P.A.P, the conflict comes from A.J. wanting her Apple family to get along among each other to give a good first impression. Pinkie didn’t fret over that and was only upset that they didn’t learn for sure that they’re related. However, come Hearthbreakers, the worry and concern does come to both Earth Ponies. Applejack felt Pinkie’s Pie Family would have been happier to do the Apple Family traditions instead of the Pie Family traditions right away. The results were a disaster and at one point, Pinkie cried, “Don’t make me choose!” [between the family she was born into and the friends who love her like one] Heck, both of them shared a crying scene in the caverns. So the verdict: Both of the episodes are excellent candidates, but Hearthbreakers put worry and conflict on both Earth Ponies rather than just one.
Other Nominees: None others

Look Before You Sleep (S1)/ Made in Manehatten (S5)
For a brief moment I’d consider replacing Look Before You Sleep with the more recent Made in Manehatten. But looking back, LBYS was a bottle episode, having just Applejack, Rarity and Twilight in a single location. Because of the small cast, A.J. and Rare have much more contrasting interactions with each other here than in their Map episode, Made in Manehatten. So, I’ve decided to let LBYS keep its title of “A.J and Rare”
Other Nominees: Simple Ways (S4), Trade Ya (S4)

Applebuck Season (S1)
It was easy to pick this episode to represent Twilight and Applejack sharing the spotlight. All throughout the episode, as A.J. stubbornly tries to harvest the apples on her own despite getting sleepy and cranky, Twilight keeps coming to her, acting as A.J.’s voice of reason to sallow her pride and accept help.
Other Nominees: None others

Bats! (S4)
Despite the unbalanced argument between the Mane ponies, this episode clearly has Fluttershy and Applejack in the spotlight. Applejack wants to get rid of the Vampire Fruit Bats; Fluttershy wants to allow the bats to have a section of the orchard; a disaster occurred; A.J. swallows her pride and goes with Fluttershy’s solution. Despite the reception of this episode, this episode is currently the only episode that clearly stars Fluttershy and Applejack.
Other Nominees: None others