I'm trying to find out which operation is fast, evaluating a comparison vs doing an arithmetic option on a single word (e.g subtract, add). Can anyone point me in the right direction with some blogs, books and other material? 
comparisons vs arithmetic complexity
algorithms;complexity theory;reference request
It principle it could depend on the processor. However, I imagine that comparison are done using the same circuitry as subtraction, so the complexity should be comparable. I'm assuming that by comparison you mean an instruction comparing two registers and setting some flags (or another register). A conditional jump might interfere with pipelining and so would be costlier.