I'm about 1.5 years and 10 basses into experimenting to find my sound. Changing strings on bass has MUCH more tonal impact than it does on guitar - finding the right set can absolutely be make or break for a bass, and I have literally moved on basses just based on having not found a string set that matches up well with the bass. Here are a few string sets I have tried.
I play 100% of the time with a pick, ymmv if you pluck with fingers.
D'Addario Chromes - the only flats I have regularly used, I have used them on 2 P's, 2 J's, and a short scale Jag. They give an excellent full range sound, with much more fundamental than rounds, which translates for me to a much fuller bottom end. They retain more top end than most other flats, and I have used them extensively with my hard rock band where I need some top end and clank. With the classic rock band, they are the best for my sound with my band, 1 guitar/bass/vocals/drums.
EB Cobalt Flats - I tried 2 sets of these. I liked the sound, a little brighter yet than Chromes, but 1 set had a dead A, and on the other set I suffered my only ever broken bass string, so they are no longer an option. They also don't like to be removed and restrung even back onto the same bass - they creak and groan when tension is added. I just don't trust them.
DR lo-rider steel - these are my current favourite, and I have a Ric and my Geddy J strung with them. They are what you would think they should be, bright and very present, but with plenty of low and low mid as well. They seem to be lasting well and retaining their sound very well also.
D'Addario Pro Steels - tried before the DRs, they were OK but missing something. Very high tension, which generally doesn't bother me but these did. The 105 E string seemed larger than any other 105 I've used for some reason, though I didn't take a micronometer to them. Some love them, but again I find the DRs superior. Pro Steels have a rep of losing their sound fairly quickly, I didn't have them on long enough to find out.
D'Addario NYXL - nickel plated steel. Definitely mellower than straight up steel, and a little less tension than many others I've tried. I have them on 1 P and 1 J, I like them best of any nickel type string I've used. They have a tremendous amount of native growl, that's not too bright, they really purr!
I have tried several other sets on various basses. I don't remember them all, other than regular EB Slinkys, which I really didn't like though admittedly 1 set is too small a sample to draw a definitive conclusion.
Funny how I love EBs on guitar and dislike on bass, and have the exact reverse opinion on D'Addario. I will also note that my body chemistry is usually easy on strings, so if you sweat a lot and 'eat up' strings quickly your experience may be different than mine re: longevity.