I’d buy TI jazz flats and try them on both basses. If you have two “four in line” headstocks and similar scale and string lengths, you should be able to swap the strings back and forth.
Keep in mind TIs take many, many hours to break in. They just keep getting better and better, but the initial install sound is very bright. Over the months, they will sound very different, and you’ll discover the huge range of dynamics they deliver. From super smooth warm, to nasty sneeze, and woody upright like sounds.
I also use DR Pure Blues .040’s for rounds. These and the TI flat swap back and forth with very little fiddling around with setup. They feel is pretty close as well.
I’ve had sets of TI flats go from bass to bass over years of playing. The price tag looks expensive, but the bang for the buck over years of play is awesome.
Sometimes you can find used sets in the classifieds.