Wake's biggest trump card with respect to both sports is its conference affiliation. Wake needs, and always has needed, the ACC much more than it needs Wake.
The issue is that the relative important of conference affiliation is trending in opposite directions in basketball vis-a-vis football. Never has being in a "power" conference been more important in football than right now, while the opposite is true in basketball. In short, Wake football is buttressed tremendously by being in one of the few AQ conferences left standing, while Wake basketball -- at least with respect to the attractiveness of its head coaching position -- has been whittled away by the success of mid-major programs like Gonzaga, Butler, Xavier, Wichita State, and VCU.
All that said, I actually would posit that both positions are more attractive than most here give them credit for. The football job has the benefit of always having a seat at the big boy table, having a chance to sneak into the Orange Bowl (if not an 8+ win season) by virtue of unbalanced schedules and an infusion of historically basketball-centric schools from the Big East, and modest if not downright realistic (!) fan and alumni expectations. The expectations in basketball are admittedly much higher, but for good reason: we are in one of, if not the, most fertile recruiting areas in all of HS basketball, few schools' alumni have greater recent NBA success than we do, our facilities are stronger relative to basketball, and financial and academic limitations on recruiting are somewhat mitigated by the vastly smaller number of scholarships in play. (This is of course to say nothing of the fact that the ACC has always been fancied as a basketball-first conference, with in-conference rivalries more of a recruiting boon than the same are in football.)
At the end of the day, the Wake basketball job is definitely superior IMO, but neither is a slouch and the question of just how good the Wake basketball job really is sort of is a moving target given the recent upheaval in conference affiliations.