I'm gonna be the odd one out here, I have only flats on my 5-string jazz bass.
I like it when other people use rounds for their tone. I just don't particularly like it when I do, although I haven't used the newer pressurewounds. Just like I enjoy other people using picks, even though I myself have cultivated my own finger-style tone and stick with that.
My flats of choice for now are the Jim Dunlop Brite Flats. Might be nice to have slightly lower tension, but I just lowered the action on my bass as far as I can get away with it. I've had these strings on for a couple months now, long enough to let them settle, and they sound earthy, sweet and still crisp to my ears.
I totally agree re: flats loving reverb. I have a reverb pedal from Old Blood Noise called the Procession. It has a couple pre-effects you can put on it, phlange, filter and tremolo. The tremolo is really where it's at for my sound when I want to use it. It's also got the sustain option - an extra footswitch you hold down after playing a note or a chord, and that sustains while everything else runs dry until you let up. With a five-string, you can do some interesting things, e.g. a low note on the B string sustained then kick on your overdrive and play an octave up.
I had never heard of the Old Blood Noise pedals before, but really think it accentuates the sound.
Also agree with setting your eq for your strings rather than trying to match strings to your eq.
If I was going to use the zingiest round strings on a four-string bass, I'd probably use Ernie Ball Cobalts. I did like their sound. From what I read though, the fifth string for those tends to break often.
I disagree with those who think us flatwound users just want an old school dead thump, someone said "like a rotting log". Well, I totally get that, I know where it comes from. That's exactly how I used to think. But newer flats really can sound good, and I found I just needed to learn how to approach the strings a bit differently.
Then again, when I played pianos, I always gravitated to the darker-sounding tonewoods, instead of that 70s bright Yamaha-ish sound so many people like. But again, I think there's a big difference between what you like to play on to achieve your own tone, vs. what you like listening to when others are doing it.
Meaning, I don't like the sound of myself on really clanky steely round strings. But who doesn't like Chris Squire? Or many other people who sound like that?
Anymore, rather than try to be all things to all people, I try and cultivate the tone I particularly prize. As long as one can be flexible enough to play in different situations and still make it work, that's fine. This is why I went with the Jim Dunlop strings, though next time it may be TI Flats if they really do still have some bite to them. I heard reviews with those and they sounded great for Jazz but nothing else. The Dunlops I can use for reggae to hard rock if I want. They respond really well to the individual tone controls on my pickups.