I had flats (heavy gauge Roto 77) on my first bass, a Squier VM fretless Jazz. Loved them.
Then I got my Squier CV 60s Precision, put the 77s on it, and didn't like them at all. Too, well, flat. Dull. Don't know why, perhaps the pickup is too bland.
Tried something completely different: Ernie Ball Super Slinkies. Light gauge nickel rounds. Lost their brightness quickly, but even after more than half a year of almost daily use they are still alive and give a nice warm tone. Sounds quite authentic playing along to Stax blues stuff. So I might be emulating what others get with flats on their P with rounds on mine.
On my Jazz (Sandberg JJ/TT Passive) I loved the Rotosound 66 for their growl, but had to set up a very high action to avoid buzz. Also I could watch them destroying the frets while I was playing. Now I'm using DR nickel Lo-Riders. A bit more mellow, but still with more character in the mids than zing up high. Just what i'm looking for. Can't imagine using flats on the Jazz for now.