Broadcast made liberal use of vintage synths, though I don't think I have ever seen any video of them with specifically Moog gear. They have, however, been filmed with a Korg Delta, Korg MS-20, and Sequential Circuits Pro-One.
Stereolab was, of course, one of the earlier contemporary bands to champion vintage Moog gear (and actually my introduction to Moog). Looks like it's only a Rogue in this video, but they have at various times made use of the Rogue, MG-1, Voyager, Little Phatty, and Opus 3.
Lali Puna are something of a sister/spinoff group of the Notwist, and use a Korg Delta and Moog Opus 3.
Black Moth Super Rainbow use a Yamaha CS-50, Octave CAT, Yamaha CS-15, Rhodes Piano, Novatron, Yamaha CS-10, Moog Little Phatty, Electrix Warp Factory, and various 'foogers.