I officially declare the 2015-16 season close enough to go ahead and rank the nation's strongest conferences.
For our purposes right now, "strongest" will mean what it usually connotes, albeit somewhat imprecisely, when tossed around by writers and fans alike: "NCAA tournament teams only." In terms of true top-to-bottom statistical strength I expect the Big 12 will continue to hold an advantage over its major-conference rivals not only because the league plays very good basketball (which it does) but also due to the fact that the conference has just 10 members. If Division I team performance is a bell curve, other things being equal it's statistically advantageous to have fewer programs that are mediocre or worse pulling you in the direction of the mean.
In other words, if the following good-teams-only projections are correct, this could be more or less how well the respective conferences perform come Selection Sunday in terms of seeding. To compile these rankings I considered seeding performance last season, returning experience (as gauged by both minutes and possessions used, as detailed here), incoming freshmen and impact transfers.