The New Big East being better off on Fox and the AAC being better off on ESPN can both be true. The New Big East schools had to separate at a certain point - they are now in a position where they are the predators in their universe (the non-FBS Division I world) as opposed to the prey in a football universe where they didn't even play that sport (which the Old Big East was) when it comes to conference realignment. There is additional value in stability, particularly when you know that you'll never be in one of the power football leagues. The Big East wasn't ever going to be a football conference, so whether the future of the college sports world splits along football/basketball lines is immaterial to them - they had to make the best basketball-focused move. At the same time, Nelson (who I rarely agree with) is correct that the NCAA Tournament is a much stronger force keeping the different tiers of Division I basketball together compared to how the Power 5 conferences legitimately would love to fully separate from the non-power leagues if at all possible. The fact that Fox is paying more TV money for just Big East basketball compared to the AAC with both football and basketball made it a complete no-brainer for those schools.
Please also note that Fox is still in a good position to become a viable competitor to ESPN (particularly compared to others like NBCSN). Remember that Major League Baseball games are heading to FS1 (including most of national game of the week package that had been on over-the-air Fox and several playoff games) along with USGA events (most importantly, the US Open), FIFA events (i.e. men's and women's World Cup) and NASCAR (not my thing, but a good number of people watch it) on top of the Big 12, Pac-12 and Champions League that they already have. We're seeing the early days of FS1 and FS2 where they have sporadic live programming (so the ratings reflect that and further depresses the ability to cross-promote the schedule), but the scale is going to look significantly different a year from now. FS1 may never end up being as popular as ESPN (in fact, I'd count on that), but that's a legit sports lineup for legit sports network for the long-term with events that draw in the casual sports fans that ESPN is so good at doing. (In contrast, NBCSN seems to be concentrating on the upscale yuppie and hipster sports fan demo with the NHL and Premier League, which I personally enjoy, but don't nearly have the casual sports fan appeal as what FS1 already has.)
Meanwhile, the AAC is still getting exposure on the ESPN platforms. There's no way that the AAC should have gone to NBCSN when ESPN was paying the same price. Taking a chance on an upstart network like FS1 or NBCSN is fine when they're providing a Godfather offer in the way Fox was doing for the Big East, but ESPN is still preferable when all things are equal. So, the AAC will still get good exposure, although Mike Aresco has a bad habit of overselling a lot of things publicly (so I wouldn't exactly trust a lot of the specific numbers that come out of the AAC PR office).
If I were running UConn, I'd still think that being a full member in the AAC is better than being a football independent/Big East basketball member simply because UConn is one of the small handful of schools that could conceivably cash in on a power conference lottery ticket. Independence is a tough road, as well. The one thing that all of the existing independents have in common is that they are legitimately uniquely national schools whose fan bases and identities have nothing to do with their respective markets or regions: Notre Dame = Catholics, Army (and Navy, for now) = military, BYU = Mormons. Independence simply isn't realistic unless you're that type of school (and not even powerhouses like Texas, Ohio State and Florida are that type of school - they might have huge fan bases, but they are still generally tied to their populous regions as opposed to being truly national).
Now, one option is to maybe join the MAC for football-only with a couple of others (i.e. Memphis, Temple) and then join the Big East for basketball and everything else along with them. I personally wouldn't pull the trigger on that move if I were running the UConn athletic department (because as fun as MACtion might be on TV, that's truly a peanuts TV contract), but that's really the only way that I'd say being a Big East basketball member could conceivably work for UConn.