Comparing for equality can use either SUB or XOR: it sets the zero flag if (and only if) the two values are equal. That's why JE/JNE (jump if equal/not equal) is an alias for JZ/JNZ (jump if zero/not zero).

There's also the TEST instruction, which does a logical AND but without storing the result (like CMP does for SUB). This can be used to test specific bits.

Testing a single register for zero can be done in several ways, in addition to CMP with 0:

    TEST AX,AX
    AND  AX,AX
    OR   AX,AX
    INC  AX    followed by DEC AX (or the other way around)

Also any arithmetic operation sets those flags, so you may not even need an explicit test. MOV doesn't set flags however, at least on x86 -- it does on some other architectures.