All of your options should sound good. I have switched to BEAD on all but one of my 4 string basses including a J a P and a Stingray as well as a Spectorcore fretless. Flats generally will give you higher tension vs rounds so you get a nice tight B string if you use Chromes or just about any flats except Thomastiks which sound great but are rather floppy.
I just went BEAD on my jazz. The P really sees all the action, but I needed a 5-er for an upcoming theater gig. That bass didn't work out; I've just gone to 4s, and I can't go back.
Anyway, I put the bottom 4 from a TI flats 5 set, and I'm REALLY disappointed with the B. Not just floppy--I don't play with a pick much, and I like the TI tension (and feel)--but there's just NO definition.
They weren't great on the 5 (I moved them) either, but I thought it was that bass. Need to find a better flat set...