Aspartame itself is completely safe, but recent studies have found all artificial sweeteners have metabolic effects. It's not that the chemicals themselves are hazardous, as you say aspartame in particular has been very rigorously studied, but that it appears the body uses the sweet taste as a signal to change insulin production.

Is it better to have a diet pop than sugar pop? Definitely and I prefer Diet Coke these days, Classic feels like drinking syrup.

However it's even healthier just to drink water, or non-caloric, unsweetened drinks like coffee or tea. Soft drinks are supposed to be a treat and not a food group, I drink maybe one a week.