This is pretty silly. I'm probably the most unbiased person here in looking at this comparison, since I went to both schools.
Basketball: 4 championships or not, KU is quite a bit ahead of UConn. More fans, bigger name, in tournament every single year. They are a top 4 team nationally with Duke, UNC and Kentucky.
Football: as bad as it is, KU is probably ahead of UConn here too, but it's close.
Academics: UConn better at USNWR, but that's mostly because of a state law in KS requiring them to accept many in state freshmen with minimum qualifications. They are AAU, and at the graduate and research level, which is what the B1G cares about, well ahead of UConn. Call it a tie.
Population: Similar. KU is very close to KC (40 miles to downtown, much less to the major suburbs) and Topeka, and has a wide ranging fan base. Storrs is almost 30 miles to Hartford.
Endowment: UConn $377M. KU: $1.86 Billion. This is often viewed as a measure of alumni interest and enthusiasm.
Campus attractiveness: Both are nice looking campuses, but as far as things to do when traveling there, Lawrence beats Storrs by miles as a college town. It's driveable from many of the schools that would be in the B1g West.
By the way, they don't really grow much corn near Lawrence. Kansas is wheat country.