There is zero reason to assume that Kakashi is weaker than Asuma especially with a Sharingan, even a three tomoe one. The statements aren't in Asuma's favour, as one of the databooks (the first one I believe) says that Kakashi is the strongest Jonin in the Leaf. The relevant third databook statements that cover early pre-Pain Invasion Arc Shippuden list Kakashi as the overall stronger, with better Ninjutsu, Genjutsu and an equal Taijutsu stat. Kakashi should win mid-diff. He counters all of Asuma's jutsu with his vast arsenal and has potential to put him under a Genjutsu.