Here's a post that I made in another thread a few days ago...
Tapewound strings (as compared to flats) will have slightly less wear on your frets and slightly less finger noise on slides and will feel slightly more slippery than what you have today. Depending on which tapes you try your sound will be at least as bright as it is with typical flats and maybe much brighter. There are a lot of different tapes out there but the rundown on the three I've used is a follows:
La Bella Black tapewounds - I like them a lot, relatively low tension, sound a little closer to flats than rounds. Nice deep dark tones, lots of thud and power in the notes (not thin sounding at all), a somewhat woody tone, good sustain, very long lasting (going on year 9 with one set), very balanced tone across all strings. Not sure how they would hold up to picks (other than felt) or slapping. A standard thickness size will most likely require filing your nut and may be too thick for through body stringing on a low B string.
La Bella White tapewounds - I love em, same low tension as the blacks, sound a little closer to rounds than flats, nice deep tones but slightly more mid focused than the blacks, not thin sounding, I assume they will last as long as the blacks, clear wrap over steel strings gives them more of a normal string look vs the blacks. Very well balanced, a little more slippery than blacks. I got a light gauge set and they fit my nut perfectly. If you are a round wound nickel player you have to try these strings they really are the best of both (flat and round) worlds in my opinion. For a great deal get them from Bassstringsonline.
Rotosound Tapes - not my cup of tea, high tension, plastic feeling, very much a dead flat wound sound on my Jazz, less sustain and not very well balanced across all 5 strings. Long lasting (unfortunately), not as smooth or slick as the La Bella tapes.
Hope this helps!