Time delay estimation between two complex signals(IQ)
Cross-correlating the absolute values of two signals will often not yield good results.  Consider the case in which you are trying to align two continuous (i.e., non-pulsed) signals.  Their absolute values are roughly constant with time.  Cross-correlating them will yield no peak.  If the amplitude of the signals changes with time, you may get a peak, but the cross-correlation will be able to exploit only the amplitude of the signals.

On the other hand, cross-correlating the complex values will yield a better result because it exploits both the amplitude and phase of the signals.  Note that you will generally need to look at the absolute value of the correlation, not just the real component, since the phases of the two signals are usually not the same.  Some complication arises if the two time-delayed copies of the signal have different frequency shifts, in which case long correlations may not yield a peak.  That frequency difference can sometimes yield useful information, however.  This is a significant topic in radar.