UConn arguably was more successful than Syracuse during the time they both shared a conference.
2004: Syracuse 4-2* / UConn 3-3
2005: Syracuse 0-7 / UConn 2-5
2006: Syracuse 1-6 / UConn 1-6
2007: Syracuse 1-6 / UConn 5-2*
2008: Syracuse 1-6 / UConn 3-4
2009: Syracuse 1-6 / UConn 3-4
2010: Syracuse 4-3 / UConn 5-2*+ won tiebreak
2011: Syracuse 1-6 / UConn 3-4
2012: Syracuse 5-2* / UConn 2-5
Both teams won conference co-championships twice, UConn claiming the only BCS bid during that time. Syracuse's co-championship years were the only years they had better conference records than UConn. Neither team was outstanding, but UConn went 27-35 during that time with Syracuse going 18-44. Syracuse's edge came with it's decades of successful history at the major college level that easily put it in the drivers seat for a spot (first in 2004, then again in 2011)
Ultimately the problem for UConn is it started "big time" football too late to build a name or history to make it attractive outside of basketball (and you could argue it's basketball success started too late to make it attractive enough to the only conference (the ACC) that still valued basketball on par or ahead of football when things started). Then taking the lead on a lawsuit, plus the misguided fear of competition from a nearby neighbor built enough animous to make the only conference still valuing basketball highly in the 2010s willing to look at alternatives (reportedly Pitt got a spot originally earmarked for UConn). Finally football first forces reportedly carried the day, the final time around.
Since then UConn made two additional hires that proved disastrous putting the football program into laughing stock range. That, coupled with a couple of unconventional decisions for a football first culture that reigns in conference governance (going independent in football & canceling the COVID season in its entirety) has led to the impression that the school doesn't care about the #1 revenue sport, creating an even bigger hole to dig out of if they are to find a desirable conference home.