I haven't been but I'm pretty much the only one in my extended family who hasn't. They all rank it as their favourite place in Europe. My Uncle has sailed around the worldl so he knows his beaches and shores and put Corsica right near the top. Him, my Aunt and my Cousins keep going back.
Its also managed to stay off the radar as a tourist spot. Almost all the people who go there are affluent Italians with weekend/holiday homes. The photos of the place look amazing, the foods supposed to be incredible (even by Italian standards) and its not packed full of tourists and the towns and villages are the type you see in brochures, rather than the reality which often isn't as picturesque.
In general the other European beach resorts fall into two types; the ultra expensive and pretentious ones like St Tropez (fun for a couple of days but thats about it) or the cheap package holiday resorts full of drunken morons (I'm guessing that if you wanted this Mexicao would and cheaper than going to Europe and be easier). Either way, they're all get really packed out and busy (St Tropex less so but for the prices you need to be it fucking well should be cheaper).
Corsica doesn't get busy, you can go and find your own little cove and stuff like that. Not a chance of this even at the really expensive French resorts such as St Tropez.
Downsides; its a pain in the ass to get too.
Also, diving in Europe is pretty crap, there are far better places to go if this is a priority. Egypt would be amazing if you wanted to dive. Its also a great place to go wake or kite boarding.
PS If you do find yourself in one of these package holiday resorts (e.g Magalouf, Ibiza) use your ears. If you hear British accents go the other. Brits on holiday are renowned in Europe for being drunken aggressive idiots.