Everyone will tell you that thief's running ability got bloggered in the update.

Some people (like yours truly) will tell you that there wasn't even much difference in the NES version.

If you're looking for an adulterous fling away from the thief, I reccomend a Red Mage, actually. The Sun Sword is only minutely weaker than the Katana, and the white magic / extra black magic more than compensates for that anyway.