I really don't think there is any difference between Osaka humor and Tokyo humor, though people of Osaka and Tokyo clearly think there is.
Osaka people tell jokes more often than Tokyo people and they thus have a better tuned sense of humor. Also their patter tend to be more rhythmical. But Osaka people talk more rhythmically when they are NOT telling jokes so it is not just the humor.
Stand up comedy started in Osaka in Japan. But stage comedy has a very old tradition (they talked sitting down) and Osaka and Edo (Tokyo) both had their own factions of them. Katsura Beicho is a master of traditional Osaka style stage comedy and is also a professor of literature at Osaka University. I once heard him explaining on TV the difference between the humor of Kanto and Kansai, but I really didn't get it.
Stand up comedians like Takeshi Kitano, who is from Tokyo, looks heavily influenced by Osaka humor to me. Especially the Yasushi-Kiyoshi duo. But I hear that the detractors of the Yasushi-Kiyoshi duo insist that they are too influenced by the Tokyo crowd.
I guess there is very little difference when it comes to humor.