3 fins are more efficient than 4 fins, if you size 3 fins and 4 fins for a rocket with the same CP, you'll find that the 3 fin configuration has less fin area and thus less drag.
One disadvantage of 3 fins is that almost any combination of angle of attack and yaw creates roll. 4 fin rockets have much less roll. The MIT Topics in Advanced Model Rocketry book goes over this in some detail.
As noted, when moving fins or control surfaces on fins, it's a lot easier to keep track of the response to control surface deflections with 4 fins; 2 for pitch, 2 for yaw, differential for roll. In fact I can't think of a guided rocket with movable fins or fin control surfaces that has 3 fins; US, Russian, etc., they all have 4 fins.
Many military systems are volume limited, and often have folding fins to fit in canisters. 4 fins have shorter fin spans than 3 fins, again for equivalent stability.
Attitude control for solid rocket motors was a major problem. The early systems (examples, Sargent, Scout first stage) used jet vanes (usually combined with fin elevons) like the V-2 and the Redstone. Other systems were tried, none (Scout, separate peroxide RCS for the upper stages), single axis per nozzle (Minuteman I, II, and III first stages, nozzles only gimbal in one axis), and liquid injection (Minuteman II and III stage 2, Titan III).
Then the big breakthrough, the Lockheed Lockroll (or named something like that) followed by the Thiokol flex seal nozzle (both very similar). The flex seal nozzle is the current definitive solution for solid rocket motor thrust vectoring. The drawing previously shown was a flex seal nozzle.
Then large solid rocket motors went from multiple nozzles (4 nozzles on Minuteman I, II, III first stages, Minuteman I and II third stages), to single nozzles as used on the Peacekeeper. One big nozzle has lower nozzle internal drag, and lower weight, than 4 smaller nozzles. Moves in 2 axes for pitch and yaw. But how do you do roll with a single nozzle? You don't.
The rocket actually rolls very little (it's asymmetric), and modern missile systems are not guidance gimbal limited, so the missile can roll to whatever angle. The final stage which has 3-axis attitude control takes out whatever roll has developed (because now it does matter), and lines up the final stage in the correct attitude for the next phase of the mission.
Chuck Rogers