OK, I've just completed 4 very different and distinct gigs into my switch to flats on my Jazz Bass. For the record, I'm using D'addario Chromes .40-.60-.80-.100., and the best way to describe my band is a "Jersey Shore" R&B based classic rock and soul/Stax sound.
First gig was an outdoor boardwalk bar show in Pt. Pleasant Beach, with my rig and the house PA. I noticed that the flats were fatter sounding out of the gate. The strings were put on the bass 2 days before, so they were not broken in. Right away I noticed more of a present mid punch with these. I have played rounds for the last 30 years, so I knew that there would be an adjustment period for me as well. First gig, these were a little "sticky" to the touch. I did like them, and was willing to keep them on for a true break in period.
Second gig was 2 days later in a club with a great stage. These strings sounded like thunder with my rig, through the club's PA system. They were (and still are) plenty bright, but not as bright as new rounds - they sound like a nicely broken in set of rounds, and sat very well with the kick drum.
Third gig was a casino gig with a house rig and PA. The strings at this gig were breaking in nicely, and really sounded great in the mix. I agree that they occupied their own "sonic space"; more than one person at this show asked if I installed hotter pickups in my bass!
Fourth gig was an outdoor show Sunday afternoon at the Jersey Shore Jazz and Blues festival, with a supplied rig and PA. By this time, the sticky feeling of the strings were gone - they were nice and slinky smooth, and I'm now accustomed to the feel of these strings and what I can do with them. I'm digging the tone of these like crazy. I can keep them smooth, or make them growl, dependent on left hand pressure, right hand placement, etc. Once I figured these strings out, I'm getting great definition and kick from them.
Thanks to this very informative thread, this is my first experience with flats. Prior, I would not have considered them. So far, I'm glad that I did.