To start, Ultear have a nice AP advantage here.
Braixen has alot of good moves, three good spamable stabs in the form of Flamethrower, Heat Wave and Fire Blast, there is also Psychock and Psychic in the form of other good damaging moves. Flame Charge, while not as good as the previous, is pretty spamable since it can amp his speed after used. Will-O-Wisp is a good lead move to halve Ultear's main form of attack (her orbs) and that would actually make Ultear weaker then Braixen in AP, while Sunny Day plus STAB would make Braixen stronger for a short period of time, even more if Blaze is activated, Fire Spin can be used to give some nice damage with the Vortex, while limiting her movements, there is Tail Whip to lower Ultear's defenses, but i don't think that this is to needed, since Braixen can already make himself stronger with Sunny Day. Magician can steal some of her Orbs, while Magic Room would just shut down the Orbs. Psychic Terrain will make his Telekinesis and Psychic attacks stronger, making Braixen able to counter the Orbs with her own Telekinesis, though Ultear Telekinesis is likely stronger, that could slow down the Orbs. Wish is a good form of recovery and Hypnosis, while that accuracy is really bad, the Sleep is a good effect that benefits Braixen alot. Braixen even resist Ultear's Ice Manipulation, making the gap in favor of Braixen.
Ultear itself has some good abilities, but some are countered by Braixen.
His Ice Manipulation is kinda useless here, give the fact that Braixen resist Ice Manipulation. Her telekinesis, as saided above, is likely stronger than Brainxen's and that can be amplified with Psychic Terrain, making it not really useful when Braixen notices that. Her Time Manipulation is relatively weak when compared to other Time Manipulation users, only affecting not sentient beings, but i am not sure if that would affect Braixen's Wand, but even if it affectedm Braixen has shown that he can use his attacks without it.
Voting another Female looking pokemon that has more than 80% of being male Braixen Mid-Diff due to versatility, ways to counter most of Ultear's abilities and stat amps and reduction