Personally I use amex for all large transactions because they give me a cut (I think around 0.5% cash equivalent?) in air miles, but don't usually bother with it for small transactions because I don't want to risk it being turned down, or take the piss with small merchants who might suffer from the processing fees.

Perhaps this kind of behaviour explains their bigger cash volume, rather than their customers necessarily being bigger spenders in total across all the cards available to them.