To be honest, that's hard to say one way or the other since total medals and gold medals have been equivalent sorting algorithms since the 80s. My recollection from watching is that total medals was always what the newscasts were talking about, but my recollection is not what it used to be.
Edit: oh good, so my recollection is in line with that wiki article. Why doesn't that make me feel comfortable?
True - weighting by popularity would probably be more "accurate" than weighting by historical longevity. That may be difficult to determine for some events, though, unless you count qualification rounds as well. For example, you can't just bring a soccer (er... football) team to the Olympics, your country must qualify first. Which brings up the fact that team sports have fewer entrants than individual sports, so would number of countries entered be better than total number of entrants?
I don't buy the "upper class sport" argument for the simple reason that if a country wants to specialize in something then they're going to do well regardless of the sport (*cough* Jamaica *cough*). The Aussies concentrate on (and do very well in) swimming... but that's their choice. You can't tell me that they wouldn't be good at Equestrian if they put their minds to it. They have a grand history of riding horses just like the US... but they choose to focus their funds on swimming.
I don't buy the multiple event argument either because winning golds in multiple events is insanely difficult. I am a former competitive swimmer (though never of any consequence) and at least in swimming the four strokes require surprisingly different techniques. Michael Phelps is a freak of nature... he makes it look easy. But the different strokes in swimming are, to me, at least as different as the 100 meter dash compared to the 110 meter hurdles.
Ultimately, there may be multiple equally valid winners. After all, the Olympics recognizes both "most gold medals won" and "most medals won" when discussing the greatest Olympians of all time. Or at least they have until now... Michael Phelps is in the process of making that distinction irrelevant, too.
Though, interestingly, many mark Michael Phelps down because he has only competed in 2 Olympics (he was an alternate in 2000) as if that somehow makes his total medal haul less impressive.