The first bass that I bought came with Elixir round wound strings, which I enjoyed playing on. Elixir strings have a reputation of durability, along with playability, which is what one looks for in a good set of strings. I began to notice, however, that my fingers tended to suffer when I did a lot of sliding on the strings with round wounds. So, one day, after repeatedly reading about several female bassist's preference for flat wound strings, I decided to try a pair out for myself. I chose a set of D'Addario Chromes in the heaviest gauge I could find. Sure, these strings cost about twice as much as round wounds, but that first set I bought literally lasted a year before I had to replace them, and that was with me playing around 3 times a week. Flat wound strings are smooth as silk on my fingers when I slide, and I still get that magnificant low end that I love so much. I don't want any brightness when I'm playing bass. I want all bottom end, so flat wounds are a perfect fit for me. I love the D'Addario Chromes, but I've also tried the Kurt Mangan flat wounds as well, and they have a great sound, too, for around the same price. I usually pay around $35 for my flat wounds, but like I mentioned before, they tend to last twice as long, if not longer, than any round wound string I have found, and are much easier on my fingers.
So, if you're not quite satisfied with the round wounds you're playing on now, give flat wounds a shot, and you'll be able tell the difference right away. You may end up loving them just as much as I do.