What makes a shotgun a destructive device, Like a Street Sweeper and USAS-12?

BATF classified them as such.  That's it.

Dave_G basicly hit it, but to expand upon his answer, the law gives BATF some power to determine what constitutes a DD by use of a "sporting purposes" test. That is, the law defines a DD to include:

[i]"any type of weapon (other than a shotgun or a shotgun shell which the Secretary finds is generally recognized as particularly suitable for sporting purposes) by whatever name known which will, or which may be readily converted to, expel a projectile by the action of an explosive or other propellant, and which has any barrel with a bore of more than one-half inch in diameter"[/i]

Since both of the reclassified shotguns involved were 12 ga., and therefore had a bore well over one-half inch in diameter, all BATF had to do was to issue a ruling recognizing them as not useful for sporting purposes.