With respect to co-rotating props( ie props that rotate in the same direction- either clockwise/ or anti), the "critical" engine is the one that ; if it fails, you will have the worst handling effects, and the highest Vmca and Vmcg, worst single-engined climb performance.
This is because the "live" engines` downgoing-blades are farthest from the a/c centre-line, and at shallow climb angles this gives a centre -of -thrust, outboard of the prop centre-line, requiring more rudder/ aileron to counter, giving more drag, etc,etc. For most American twins/4`s , the critical engine will be No1,( from the cockpit blades rotate c/w).
A/c which have counter-rotating props have either; no critical engine,or both are critical, depending on whether both engines rotate inboard(at the top of the arc) or out board. Where you have counter-rotating props , they will mostly rotate inboard; only the P-38 is different.