I think it depends on the type of depth you have, and the type of stars you have. If your depth involves a lot of complimentary players who excel at different things, that may enable you to better exploit the weaknesses of other teams from game-to-game. This may be less useful in a long playoff series (hence why stars win championships, and depth wins regular seasons), but even then it can still help your team be more adaptable within a longer series. On the other hand, if your depth is really just backups at your positions, and the offer more of a "not-as-good-as-the-starter-but-similar" quality, then I think you're in trouble, because your depth just limits the dropoff from your starters, and your starters aren't as good as the other guys.
On the other hand, those type of backups may be good on a top-heavy team, because if one star goes down, or has to play limited minutes, the backup can come in without forcing a change of scheme, and that continuity will allow the remaining stars to operate at near their maximum level, instead of trying to alter their game to compensate for the missing player.
Of course, the other point is how good are your stars. If we're talking about mid-career perennial mvp candidates and hall of fame locks, like LBJ now, Kobe a few years ago, or 90's MJ, then yes please, star players always. If we're talking about the next tier or so of players, such as Josh Smith or Deron Williams, then making them the centerpiece of a deep, versatile team might make more sense than merely getting backups for them, or trying to pair them with other stars of that level. (Of course, there are some on this board who think that Deron and/or JSmoove are the cats meow. I think they're both good players whom I'd be happy to have on the Celtics, but find neither transcendent players.)