Absolutely TI flats if I'm using flats. I've been through just about every other brand of flats I could find because I kept putting off paying that much more for TIs and I wish I'd done it sooner not just because of the money, but their sound, feel and consistency.
I use rounds on two very different kinds of basses, a Warwick 5 and Fender J 5 and I now only use Marcus Miller DR Fatbeams 40-120 for both.
I initially tried them because I became fed up trying so many different roundwound strings chasing that tone and feel I knew existed but wasn't finding. I've modded both basses, which made great inprovements for both and still I'd say the best roundwound strings I had found after all was said and done were maybe overall 70% satisfactory and we pay too much money for bass strings for that to be acceptable.
I wasn't aware MM had signature strings and I had moved away from DR bass strings, but love them on guitars, so when I happened upon them, I figured for ***** and giggles, since I'm a fan of his, I had nothing to lose at that point and gave them a shot. I don't buy instruments and accessories from signature series because it seems more of a marketing ploy at this point, but I will say I got these solely based on the signature artist.
Initially, they were a little rougher on the fingers than expected, but took no time to adjust. The first thing that stood out to me was how I got bright and punchy, all the mids I could ask for and still had the boom that I love, especially with the low B. For me, the best quality in these strings is their physical responsiveness and consistency of tonal quality over time, especially so in that the 120 low B doesn't flop like a wet noodle. It's the cleanest, most responsive low B for picking, fingers and thumping I've played to date but isn't super high tension either.
Aside from changing sets of strings sooner than necessary out of frustration, I tend to push roundwounds on bass and guitar as far and long as I can.
TI Flats just seem to get better with age for me, though I use them specifically for surf music, but I've had my current set on for about a year and a half and they sound so good with that range you're looking for.
I think you'd find what you're looking for with either set because their versatility suits to what style you play so well.
Good luck!