I've seen unexplained lags of the type mentioned here on both about equally. In some cases I've had someone who was on the very same Google Apps for business plan email me, and then send a forward of the original when I reported I had not seen the first mail 10 minutes later, after which I received the 2nd mail immediately and still didn't see the original mail until like 30+ minutes after that.
I never bothered to follow up with Google's support on apps for business with the lag issue because it didn't happen that often (at least not that I noticed) and also I view Internet email as an inherently laggy system (though in practice it is near instant most of the time), so maybe if you do complain they'll do something, but I don't think just switching to the Google Apps for Business plan is an immediate cure for this guy's problem.
That seems to be much more what he's asking for or expecting out of a paid service, not "here, take some money for what I don't currently pay for".
Have you thought about this yet?