With the incredible wealth of talent at the point guard position, it can be easy to surmise that the most important and most pivotal position is at the 1; at the very least, it can be assumed that the balance of power has shifted from the interior to the perimeter. However, rumors of the demise of the big man have been greatly exaggerated. In fact, there's a strong resurgence of talent at the big spots, and the quickest path to contention still is centered (no pun intended) around size up front.
Of course, the biggest impact that bigs have over perimeter players comes on the defensive end, for two reasons. First (and more obviously), the size advantage allows for bigs to have a better chance of making tougher contests on shots, as well as a better chance at corralling ensuing rebounds.
The second point is more important, yet subtle, and has to do with positioning: Because bigger players are more likely to be around the basket area, much of the offensive action is channeled toward them. In other words, while a team offense can be designed to avoid an elite perimeter defender (much in the same way a quarterback can choose not to throw to the side of a shutdown corner), it is almost inevitable that the offense will have to find its way toward where the big is -- it cannot avoid him (barring the use of running high pick-and-rolls or featuring stretch bigs).
As such, it is much easier to craft an elite defense around a defensive anchor big, who can compensate for and subsidize lesser defending teammates by the simple geography of his position on the court, as opposed to building it around an elite perimeter defender (or even defenders).