I love flats, specifically cobalt ones...their sound has a bit more bite to my ear, kind of 85% flats with a 15% rounds edge to them so playing with the tone has more range in terms of making an older flatwound sound (reggae, motown etc.) and a more modern sound (pop, rock, metal etc.).
Can't comment on gigging as I don't, but for home playing I'm a fan. They go through a "sticky" phase in my experience, where the strings are quite sticky for fingerstyle playing on the right hand, after that they feel good.
I don't play a huge amount of rock but I've always liked the finger sound of mine for things like Queen, Outfield, Meatloaf and with a pick for the harder stuff like G'n'R up to metal bands.
Typically I'd go with the treble all the way down on an amp, up the bass and mid 10% from neutral and the tone all the way down on my bass. Then just roll up the tone on the bass as the songs get heavier.