When might looking at rising edges perform better than cross-correlation?
Using the rising edge is better than cross-correlation when there is the physical equivalent of an inductor in the system, which will introduce inertia into the system.  That inertia will cause the output to rise gradually, then fall back down.  Even in that case the cross-correlation might be more useful, but if you wanted to know when the input starts to affect the output the rise would be more accurate.



The figure above is illustrative of what I'm talking about.  The inductor (or "inertia introducing object") resists any change in the current flow, so initially it resists the flow causing an exponential rise (as opposed to a sharp rise that matches the presumed non-ideal impulse at the input), and then opposes the current stopping when the input ends, causing the exponential fall at the output.

If the input looks more-or-less like an impulse function, it will correlate most strongly with the output at the output's peak, at time 100.  It's clear, though, that the input starts to affect the output at time 1.  In different situations, either measurement could be the more useful one.