I remember the editor at the Norwegian science news website forskning.no praising the "diet" fizzy drinks in an editorial- she admitted it was biased as she was quite addicted herself. Anyway, while trying to find back to it through google I found lots of other stuff (all of the links below are in Norwegian):

• People drinking fizzy drinks die in a younger age regardless of weather the drinks are with sugar or with artificial sweeteners. The article concludes it's best to drink water when being thirsty. The study is also commented at nettavisen, they have more emphasize on that the cause may not be the fizzy drinks themselves, but that the drinkers in general probably eat less healthy on average.

• One does not get fat from drinking sugar-free fizzy drinks. The article still recommends to drink water if being thirsty.

• A viral story that the "diary" fizzy drinks causes blood clotting and Alzheimer is fake news

So in general ... aspartame probably won't kill anyone, though, why not drink water instead?