i have a mule bridge and a set of riff raffs in two of my flying vs. basically i fully agree with twinfan, but i'll explain in my own words ;)
to speak of 'vibe'. the riff raffs have a strong, yet transparent character (if that makes sense). they really smell strongly of late 70s hard rock IMHO. in that sense, i regard the riff raffs as being a bit more specialist, even though they remain very versatile pickups.
(the stormy monday and riff raff necks are very similar actually)
the mules are warmer, with more mids, but that just makes them more versatile than the riff raffs because of the rich fullness of the tone. for me, mules are the ultimate pickup. i never get tired of the sound, and i can play literaly any style of music with them and they always sound good. AIV magents work really well in the mules, i wouldn't request AV myself.
riff raffs are a little bit hotter, with more bite.