I've got a couple of basses that I use with different strings. My main bass (the one covering half my face just over yonder <--) is a Yamaha BB735A. I've currently got a set of GHS Pressurewounds on it that I think are going to be what I keep on it. I found the standard 5 string set to be a little too heavy so this is a modified set, the .044-.102 four string set (what GHS calls "Medium Light") along with the .128 B string that comes with the standard medium gauge set. It's actually a bit better balanced in tension, and I prefer lighter strings in any case. I wish GHS sold this as a set, it's a bit pricier to buy a 4 string set and a single B string, but I just didn't get along with the mediums.
My other bass is a 4 string Fender P bass, which wears Labella 760FL (.043-.104). It's had that set on for about a year and they are just perfect buttery smooth flatwounds.
I've got a third backup bass, an Ibanez SR800, that needs a set of rounds but I haven't settled on the right ones. I don't typically like rounds but I do want to have that as an option available, should the need arise.
I've discovered through trial and error that I have a few preferences when it comes to strings, namely: 1) stainless steel or nickel/iron alloy, straight up nickel plated isn't my jam; 2) flat or pressurewound, rounds are too zingy; 3) slightly lighter than .045-.105