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Joker with imp powers-
https://static.comicvine.com/uploads/original/11112/111122896/4691354-emperor_joker_by_junito619.jpg
v.s.
Batmite-
https://static.comicvine.com/uploads/original/5/52117/1195386-batmote4.jpg

Joker.

As noted in the story bat-mite actually was a small portion of jokers power.

As Mungi pointed out: Bat-Mite = "one little bit" of Mxy's own power, whereas Joker = 99.9% of Mxy's own power... So EJ definitely has the power advantage.

That said, this is still a stalemate, imo. Joker may have more raw power at his disposal, but even Mxy himself was unable to kill(or even harm) Bat-Mite -- despite unleashing a blast that destroyed the whole damn company of DC comics. IOW, Joker has no realistic way to 'win'(he's still a n00b with Mxy's power, remember), and neither does Bat-Mite(he's weaker, remember)... Not even a battle of pure attrition will win the day. /shrug