I've had 11 rounds on my archtops for over 20 years, used D'Addario XL's for a long time, then discovered the virtues of pure nickel strings with oldschool single coil pickups, and have been using Pyramid roundcore 11's for about four years now.
Strings are a matter of taste, the kind of guitar sounds you go for, style of music, etc...
Flatwounds are an acquired taste. I never use them on stage because for me, in a Rock and Roll setting, they're plain not loud enough, but I hàve used them in the studio, and I keep the occasional set of flats on one of my guitars. I don't like the typical "bleep bloop" smooth dark "Jazz" sound a lot of people get from flats, but I do like flats a lot with bright single coil pickups like strats or teles, or indeed the DeArmond pickups in my 61 Starfire III.
You can get a very dry hard twang from flats and single coils, like what you'd hear on a 50's Honky Tonk Country record, good surf guitar sounds, vintage rock sounds that aren't as bright and jangly as a lot of modern cleaner tones. That said - there is a persistent myth about flats that in the earlier days of electric guitar up to the late 50's, flats were the standard guitar string, all you could get, and that's just not true. A lot of Fenders *shipped* with flats, apparently, but I think that was more a case of Fender pushing their more expensive string choice than anything else.