Hi, generally if we want to compare two or more methods we evaluate first the stability of our target compounds in the selected solvents (for extractions)  that will be used by the 2 methods (during the predicted time of analysis); stability as standard compounds and in sample (s).  After we know the the target compound is stable in the selected solvents, we will compare matrix effect, extraction recovery, time and of course cost. Best regards

robustness against changes... correctness, precision, and amount of labour needed might be other ones.