I have never liked type A for transmitting much torque. They work great for driving encoders. It's a spring and thus would have some ''windup''. Also I don't like keyways and setscrews for couplings.
Type B will transmit a lot of torque, and also is easy to disassemble when needed. The full around clamping action of the coupling on the shaft is more robust than a keyway and a setscrew.