Aside from unmanned operation, what can the X-37 do that the Space Shuttle can't? The X-37 is much more maneuverable in space. It can perform rather large changes in orbital plane or shape after weeks or months in orbit. This is very useful for space-based reconnaissance.
Something I don't understand: if the Air Force wanted to keep the X-37 launch altogether quiet, why did they launch it from Kentucky Fried Space Center instead of Vandenberg? Vandenberg AFB will be the normal and typical X-37 launch location.