This is what I've found too and why I tend to keep a lot of gently used sets on hand. Every one of my basses seems to have a different set of strings that it prefers. I used to say that this or that was my favorite set of strings but have wised up and now listen to let my bass tell me what is its favorite set of strings. That said, I can still say I'm consistently a tapewounds/flatwounds guy, which at least narrows the choices down a bit. Still though, they all sound and respond differently on different basses.
I'm all over the place on mine.
I have found for my two five strings, both Fender Jazz basses (an MIM Active Jazz V and a American Pro II) that the D’Addario NYXL 45125 Light Top/Medium Bottom Long Scale - .045-.065-.085-.105-.125 are the win.
For my Sire V7, my Warlock kit build, my Ric kit build, my Ric 4003 copy and for my G&L L2000, I use the D’Addario NYXL 45105 Light Top/Medium Bottom Long Scale- .045-.065-.085-.105 because they work great in all ways.
For my Carvin LB-70, SBMM Ray24CA and another kit build, I use my old favorite, the SIT Nickel Powerwounds NR45105L - .045-.065-.085-.105.
For my '74 Ric 4001, I went through about three different sets (including Labella Low Tension Flats) before landing on the D’Addario XL Chromes ECB84 Long Scale Custom Light - .040-.060-.080-.100 because they are fantastic on that bass!!
My Fender American Standard Precision wears La Bella 760FS Deep Talkin’ Bass Stainless Steel Flat Wound Standard Long Scale - .045-.065-.085-.105 because...yeah...they're just classic.
All four of my short scales are sporting D’Addario XL EXL170S Regular Light Short Scale - .045-.065-.080-.100.
The little Glarry GW101 still has the stock, crap Chinese strings it came with because I have yet to find anything that works on it.
Probably WAY more than you wanted to know, but there it is.
The closet currently has the Low Tension Flats and another set of higher gauge Chromes in there, as well as another, unused set of SIT Flats that I bought before I switched to the Labella Deep Talkin' Flats on the Precision.
As you can see, though, I have definitely 'played the field' when it comes to stings on my basses. I know that 20 years ago, before landing on the SIT Nickel Powerwounds, I tried strings from Dean Markley, Ernie Ball, Dunlop and at least two other brands I can't think of right now.