I'm guessing you want to keep whichever you choose around for the end of the game, so some of the reasons I point out will relate to the Elite 4 and Champion, not just Brycen's Gym.
Mienshao
-STAB attacks super effective against Brycen, Grimsley, and quite a bit of N's team
-Resists Grimsley's main STAB
-Can learn moves like U-turn for Caitlin, Acrobatics for Marshall, and Stone Edge for N's Reshiram
-Excellent Ability in Regenerator, especially when paired with U-turn
-Wide movepool, with things like High Jump Kick, Acrobatics, and Fake Out
-Incredible Attack and very good Speed
-Very frail
Chandelure
-STAB attacks super effective against Brycen, Shauntal, and a bit of N's team
-Resists Brycen's and Marshall's main STAB
-Can learn things like Energy Ball to cover many of its weaknesses, Psychic for coverage, Will-O-Wisp for crippling, and Shadow Ball and Flamethrower for STAB
-Flash Fire allows it to switch in on expected Fire moves without taking damage
-Pretty solid move variance
-Phenomenal Special Attack, respectable defenses, and decent Speed
-Less-than-decent HP
-Learns no moves by level up once a Chandelure
Both are very, very good. I used both in my Unova playthrough, as a matter of fact. I'll give sets for both:
Mienshao @ no item
Ability: Regenerator
- Fake Out
- High Jump Kick
- Acrobatics
- U-turn
Chandelure @ Charcoal / Spell Tag
Ability: Flash Fire
- Shadow Ball
- Flamethrower
- Energy Ball
- Psychic / Will-O-Wisp
Hope I helped!
