I think its a far more complex discussion than just 'this class is faster'. I'd put money on the table to wager that WDs are faster than WW Barbs in low MPs, but in higher MPs its the other way around. Obviously, for similarly geared characters. So I guess the discussion should be 'what class farms faster MP0-3' and so on.
Anywho... on an overall basis, ranging from MP0-10, I'd say, in a very very close race (as in a difference of maybe 1-2 million xp/hour or so), this:
1. WW Barb - pretty much tops all the way
2. CM Wiz - starts to shine on higher MPs
3. TR Monk - well-rounded
4. Cookie-cutter DH - tougher times in higher MPs
5. Acid Rain/Bears WD - mana problems in higher MPs only thing holding back (not applied to uber-geared folk)
WW barbs cannot efficiently get quality loot since they have to keep moving along with mobs dying in their wake, dropping potentially great rares off-screen. Sure they can kill things fast and run through content at blazing speed, but they can't pick everything up.
Archon (Teleport) wizards are slower in terms of run speed, but they can AOE everything on-screen in a single click and pick things up without losing much time. CM-WW is reliable, but not for pure farming speed.
Tempest Rush monks can easily compete with WW barb speed and they also have the advantage like Archon wizards to just chill and pick things up without worrying about losing much time.
Legacy Nat's DHs are blazingly fast since they can ToC Vault+Tactical Advantage through the entire map. Cannot compare with high spirit TR monks or insta-kill Archon wizards (since DHs have to stop-shoot-change positions more often, even when equally geared), but still highly efficient.
Same with nuke (Bears) WDs. They may be slower than the rest above, but they can still clear content fast and rely on Spirit Walk to cover great distances.
Also, no one in their right minds will loot farm on high MPs. It's not worth it for the bonus item drop %. Listen, I've tried it on my wizard and monk (not yet DH), ranging from MP1 to MP 7 with my Archon wizard (and MP10 with CM-stunlock) and up to MP5 with my monk. You get a small handful of more drops, but they're not going to guarantee better rolls. With everyone farming MP1-3, properly geared characters will be able to clear set Act III routes in 10-15 minutes tops regardless.