What are the pros/cons of all-moving rudder?
All-moving control surfaces are like regular surfaces, only that the moveable part extends over 100% of the chord. Since the effectivity of a control surface grows with the square root of the chord fraction $\lambda$ of its moveable part, an all-moving (also called full-flying) control surface has twice the effectivity (defined as normal force change per degree of movement) of one with a 25% chord length of its moveable part.



Effectivity of a control surface over chord fraction $\lambda$

Hermann Glauert was the first to calculate the inviscid lift due to control deflection, and the result of his work is shown above. The truth (as defined by wind tunnel results) is somewhere between his curve and that of my simple approximation.

Control surface in subsonic flow

Deflecting a flap causes the camber of the control surface to change. This is a positive effect in subsonic flow and allows the resulting airfoil to create more lift in the desired direction. Also, the orientation of the leading edge is maintained, causing much smaller suction peaks there than when the full surface is deflected. Suction peaks require a long pressure rise, which promotes flow separation when its gradient is too steep.

Control surface in supersonic flow

In supersonic flow, camber increases wave drag, so the full-flying control surface is more effective. Pure supersonic flow has no suction peaks, and flow separation is less of a concern. Therefore, full-flying surfaces are better for supersonic flight, while hinged surfaces are the better choice in subsonic flow. Especially in transsonic flow, at least a moveable stabilizer is necessary to avoid control reversal due to the contour break of a hinged control surface.

Stealth aircraft

Stealth aircraft benefit from large, coherent surfaces, and the gap of a control hinge will increase their RCS. Even subsonic stealth aircraft like the Lockheed F-117 and the Northrop Tacit Blue use full-flying control surfaces for their ruddervators, as does the supersonic Northrop YF-23.

Why the SR-71 rudders are special

An intake unstart at Mach 3.2 is a violent event, and the SR-71 needed all the yaw control authority available to compensate for the sudden asymmetric loss of thrust. Its rudders were optimized for supersonic use, and the actuator could be driven to its extreme position by an explosive charge which was fired automatically when an intake unstart was detected. To ensure optimum intake operation, the engines were positioned at mid-span, and the yawing moment of thrust changes was much higher than that of conventional fighter aircraft which have their engines close to the centerline for better roll agility. In addition, they use their rudders mostly in subsonic flight; only the size of the vertical tail is determined by yaw stability at top speed.