I did a check of Uconn losses in the NCAA tournament this century - there have been 11 out of 20 tournaments (100-11 record, 18-3 prior to FF.) Of those, AZ last years stands out as the only team to beat Uconn with no previous experience against them. The other losses:
ND - 5x played Uconn at least once every year in the regular season prior to those losses
Stanford - 2x 2005 loss was the first game in eight years second loss was second time in the season they met.
Duke - 1x - had played twice in regular season over the past 3 years
LSU - 1x had played early the same year (part of a string of 5 years meeting in the regular season - 4 home/home and 1 neutral.
MsSt - 1x had met in the NCAA the previous year.
So experience in terms of playing against Uconn is generally a good thing if you want to beat them - the 2005 loss to Stanford was in the S16 with Uconn as a 3 seed at the start of their last 'dark period' and Uconn just wasn't that good. Which does make the AZ win last year unique.
NC St has not played Uconn since an NCAA tournament game in 2007 prior to Moore's arrival, and Chattanooga has only played Uconn since his departure, so both players and coach are new to Uconn. I think that gives Uconn a slight edge. The fact Geno has coached so often and except for freshmen and Dorka the players have played in the E8 game is also a slight edge.
NB - of the 11 tournament losses this century almost half were in OT - 5 of 11 (ND 3 of 5, MsSt 1of 1, Duke 1 of 1)