There are certain basses and certain styles of playing that happen to sound awesome with flats. For me, particularly, I love the tone of certain recordings where a pick was used and, I presume, it was flats (although I could be wrong).. for example Funeral for a Friend / Love Lies Bleeding (particularly the Love lies bleeding half of the double track), by elton john's band. that bass tone is amazing.
Wings.... speed of sound.... I'm presuming that is flats on a rick... finger style I think, and just amazing.
things like that always make me go... oh yea, I forgot how cool that sounds. tons more examples of course.
But for playing and for my own tone, I always want very bright and full rounds. Rounds are much lower friction... remember that friction is not the same as roughness/smoothness. They are rougher and some are outright sharp edged and hard on the hands... but they are much faster to slide up and down on due to having less surface area and therefore lower friction.
Those things I notice, so I like rounds better for feel.
Tone wise, I like the versatility of rounds, and I find that many sound incredible as long as I am playing a great sounding bass. So I'm never feeling lacking in tone by playing rounds.
But some basses I've played literally required flats and wouldn't be right without them... more often than not being older, shorter scale, hollow body basses. and amazing, just amazing. And some flats can have extra meat in a lower midrange area that is super awesome also... but then so can some rounds.