Nothing wrong with trying what you already have if you like the way they sound and play.
Our band tunes down to E flat. I’ve always preferred lighter gauge strings, and I’ve never found it necessary to go to a larger gauge or higher tension string. Depending on the instrument, you might have to tweak the setup, because of the slightly lower tension at a lower tuning, but you probably won’t need to. If there’s something you don’t like about playability that you can’t fix by adjusting the truss rod, you can always try a different set to address what you don’t like. In that case, it might be worth trying the next gauge up in the same type of string (if you’re digging the current set).
The only tonal change to anticipate with down-tuning is the potential for more fret buzz due lower string tension (“floppier” strings) and the minuscule amount of neck straightening from decreased string tension. For this reason, I always set my basses up in dropped tuning; the negligible change in action when tuning back up is something I don’t really notice and when I tune back down for gigs and practices, there’s no buzz.
