Not quite. Chocobo Jig and Mazurka wear off the instant one performs any action on a mob or when a mob lands any attack or spell. Movement Speed gear doesn't wear off. It's nice for kiting in a pinch, pulling mobs, outdistancing mobs that are a waste of time to kill, and general running around (lots of running around in FFXI).
Also, Chocobo Jig and Mazurka stack with Movement Speed gear. Chocobo Jig and Tandava Crackows together give you roughly +37% movement speed. It's sexy. :3
Drops from Ironclad Cleaver in Abyssea - Attohwa Chasm. You can never go wrong with +movement speed. This update finally gave movement speed gear to the final two jobs who were missing it: Dancer and Bard, justice!