When I was in high school (late 80's) I joined the jazz ensemble. I used my own bass, which had roundwounds. The school had a horrible bass, with a bowed neck and an ancient set of what I took to be flats. But they felt nothing like any flats I've played since. Looking back on it through the fog of memory, I believe they may actually have been tapewounds. I have no idea what tapewounds feel like, as I've never played them since. Whatever they were, they were HORRIBLE. I mean, your finger stuck to them worse than Rotosound 66's coated in molasses. The exact opposite of what you think when you think "flats". And I spent the next 15 years or so assuming that's what flats felt like.
Then I had a band with two bass players. One of the reasons it worked is because I was all about bright and modern, and the other dude was all about old-school thump. Naturally, he had flats and a foam mute (on an Ibanez Soundgear
). Of course, if you're in a band with another bass player, ya gotta try his bass, right? And so... oh... THAT'S what flats feel like.
Nowadays, I have 7 basses. I have flats on three of them. They feel wonderful, just silky smooth, and give that old-school tone. But my main "originals" bass, a Carvin LB76W, has nickel rounds (DR Sunbeams). They're a nice balance between warmth and slapability (yes, I'm one of THOSE guys.
My Fender Precision has LaBella's, and I use it for blues, r'n'b, reggae, and classic rock.
My Carvin LB76 has Carvin flats, which give it a really "woody" tone, and I use it mainly for jazz.
And my Aria Pro II fretless has D'addario Chromes. I use fretless bass mainly for destroying my own self-esteem.