At what speed or altitude does an aircraft become more efficient as a rocket then a plane using thrust vectoring instead of the wings to steer? At what altitude did the flight control surfaces of the Space Shuttle become useful again or X-37B is still useful?
The answer depends a bit on the design of the craft in terms of control surfaces/wings. Atmospheric reentry begins at the Karman line at an altitude of 100 km (62.14 mi / ~ 54 nautical mi) (327,360 feet) above the surface. Which is generally when air resistance starts to matter but that does not mean control surfaces will do anything at precisely that altitude. In terms of practical vehicles that have been flow:
At an altitude of approximately 30 miles [158,400 feet/50km], the orbiter makes a series of maneuvers and S-turns to slow its speed. At 9.5 miles in altitude and at a speed of Mach 1, the orbiter can be steered using its rudder. The on-board computers fly the orbiter until it goes subsonic (slower than the speed of sound: Mach 1). This happens about 4 minutes before landing.
So somewhere up around ~175,000 feet, practical control surfaces start to work. Its possible aircraft could be built to get above this region but they would need the ability to either fly up there or survive the decent which is a whole different can of worms.
Speed: Any speed so long as your thrust to weight ration is greater than 1. All rockets start from a speed relative to ground of zero. Rockets simply have engines capable of providing 100% of the thrust needed to move (generally directed in the up direction). Planes have enough thrust to overcome drag then use the wings to help them with the lift (up direction) portion of the problem. There are aircraft that have a thrust to weight ratio greater than 1 and are capable of "flying" in a way without wings.
Speed or altitude is relative. To me the answer to this question is "At whatever speed or altitude the flight control surfaces cease to be effective due to insufficient relative wind or atmosphere and only thrust from the propulsion system can have an effect on the craft."