I think a more interesting case would be if you stripped the various FF villains of their powers, and threw them in Arkham. How would they interact with the various Bat-Villains?
"So then," says the Clown Prince of Crime, "who exactly the hell are you? I can tell you're going for the whole demented clown routine, but I thought that was my shtick! Well Harley's too, but since she's my lady friend/punching bag that only makes sense. Frankly you make
me look subtle! I may have a penchant purple pin-stripe tuxes, as well as murder and general mayhem, but you dress so flamboyantly even Liberace would be begging you to tone it down!"
Hands clasped behind his back, Emperor Gestahl's former attack dog flashes a wicked grin before replying, "Kefka Palazoo, former general and court magician, as in wielder of actual magic, not sleight of hand, in service to Emperor Gestahl. As I always say, 'Nothing beats the sound of a thousand voices screaming in unison!' If you're wondering yes, Gestahl actually let me dress like this as general. Both in the field and in the war room!" Kefka finishes with a shrill laugh.
"And to think people call me The Joker!" Joker says with an amused huff. "Well, did you kill the idiot then?"
"Oh I tried to," Kefka wistfully replies, "but alas I failed. We were on a floating continent waiting for a pack of rebels called the Returners so we could ambush..."
"For the love of drowning puppies, kittens and little children, don't tell me they honestly called themselves the 'Returners'!" Joker says, "That's the stupidest name for a group I've ever heard yet! Believe me pal, I've heard some real dozes! Like the Doom Patrol and that Brotherhood of Dada."