I need to time align two complex signals. I have two complex signals(IQ) and I need to do delay estimation and apply correction on one of the signal.

Cross-correlating the absolute values of two signals and finding the peak gives one answer while cross-correlating the complex values and then finding the peak from the absolute value of the obtained (complex)correlation gives another peak?

Which method shall I choose? what is the best way forward? Any insight into it?