^ No, I don't. It may be completely imagined, of course, but I've talked to several people who, independently, felt the same way about diet soft drinks.
Oh I'm not suggesting you're making up the effect - I'm just saying that your mate's hypothesis about it being related to the size of aspartame is erroneous. It may be a chemical result of the sweeteners, reacting in a specific way in your mouth, but it won't be anything to do with aspartame being 'big'. On your body's chemical scale, aspartame is a fairly small player.