Here's my brief analysis:
Battle Frontier Overworld - OK, I guess. It definitely contributes to the sense of accomplishment and excitement you feel when you get to the Battle Zone for the first time, but it being not exclusive to a single area ends up making it a bit repetitive. Still good.
Battle Arcade - this one's weird for me, honestly. It's special and very unique, that's for sure, but at the same time it's all over the place, lots of different eclectic sounds. Lots of extremely short segments are mashed into the song. I'd rather have longer, expanded-upon ones. It is fitting with the atmosphere and I get why people like it so much.
Battle Castle - it sounds fine, but I think other locations like Hammerlocke do a much better job portraying majestic medieval stuff. It's a bit underwhelming, tbh.
Battle Factory - absolutely fantastic... until it starts sounding like a Chinese dojo. Seriously, go look it up. There's a point where it stops being a top-notch tech facility and transforms into Greta's summer vacation hideout.
Battle Hall - incredible. Sublime. Magnificent. It keeps adding layers of content from the very beginning. Very fitting as well with the fashion catwalk. I could go on and on praising this theme for its brilliance (literally). Possibly one of my favorite non-battle themes in the game. I'm making it so difficult for you to guess what I'm voting, right?
Battle Tower - ending with a sweet note, it's a great take on a classic, standard facility. Nothing else to say, it gets the job done perfectly fine.
What about you guys? What do you think is the best Battle Frontier OST? Please do justify your choice in the replies, looking forward to them!