I actually joined this forum just now so that I could chime in on DR flatwounds. They really do have some confusing labeling (High-Beam vs Legend, Hex vs Round), but I think they only make one kind of flatwound strings (with a short-scale option), and I think they have a hex core... I don't know!
I've been playing roundwounds exclusively for a long time (my favorite are DR Sunbeams), and I recently made the switch (permanently, I think) to flatwounds. The DR Legends were the first flatwounds I tried, and I was actually alarmed by how dull they sounded in comparison to roundwounds. I did appreciate the one tone I got from them, but I felt that they would be far too limiting for a variety of musical styles. I tried a few other major brands, and I was pretty sure the D'Addario Chromes were going to be the perfect strings for me, but in the end I went back to the DR Legends.
The tone you get from new Chromes is really extreme, and I don't think it's fair to evaluate them until they've mellowed. The difference between new Chromes and new DR Legends is completely night and day, but the aged tone of both is much closer than I initially expected. The Chromes do retain a bit more "parp" in the attack, and I think they have a more extended upper-mid sustain, but I far prefer the way the DR strings look and feel. They're so much smoother and more pleasant to the touch than Chromes, in my opinion, and I appreciate the simple brass ball ends and gold silk wrapping. The Chromes actually looked and felt surprisingly cheap in comparison, to me.
To be honest, I think I might slightly prefer the tone of broken-in Chromes, but the DR Legends feel five times as good to my fingers (and look twice as nice). With a little amp EQ they can sound all the ways I want them to sound (never really bright, but very focused in the range they occupy), and they're not at all as limited as I first thought. They sit in every mix I've done really, really well with almost no effort.
I just ordered two more sets, and I think that'll take care of me for the next ten years!
Edit: Well, it's been only a very short while since I sang the praises of DR Flats (round core, I now think), but I thought I should mention that I have become a huge convert to TI Jazz Flats. They were one of the strings I had tried earlier, and I really didn't like how floppy and loose they felt, but after giving them another chance I can't believe I ever didn't love them. The low tension does take some getting used to, and the tone might too, at first, but once you get past the initial weirdness they are absolutely incredible. They sound astonishingly good on a p-bass, and if you're wanting more thump and vintage low end, put some foam by the bridge, and you'll be in Jamerson-tone heaven.