Hysteria around the aspartame in diet drinks is not justified by the evidence
It is quite hard to prove a negative but the simple observation that hundreds of millions of people take aspartame containing drinks every day without apparently causing any notable epidemiological evidence of all the effects should be of some significance. As far as I can tell no such evidence has ever been presented and most of the "evidence" is merely anecdotal.
Here is what a 2004 BMJ editorial said about the evidence:
Evidence does not support links between aspartame and cancer, hair loss, depression, dementia, behavioural disturbances, or any of the other conditions appearing in websites. Agencies such as the Food Standards Agency, European Food Standards Authority, and the Food and Drug Administration have a duty to monitor relations between foodstuffs and health and to commission research when reasonable doubt emerges. Aspartame's safety was convincing to the European Scientific Committee on Food in 1988, but proving negatives is difficult, and it is even harder to persuade vocal sectors of the public whose opinions are fuelled more by anecdote than by evidence. The Food Standards Agency takes public concerns very seriously and thus pressed the European Scientific Committee on Food to conduct a further review, encompassing over 500 reports, in 2002. It concluded from biochemical, clinical, and behavioural research that the acceptable daily intake of 40 mg/kg/day of aspartame remained entirely safe—except for people with phenylketonuria.
For those who argue that aspartame releases toxic substances in the body when metabolised (though it is hard to see how natural amino acids are toxic) it is worth bearing in mind the doses involved in typical diet drinks. This lucid explanation and summary of actual evidence appeared in the BMJ in response to some of the more hysterical critics of aspartame who criticised the editorial quoted above (my emphasis):
Mercola talks about “flooding the brain” with amino acids, presupposing that aspartame causes excessive rises in plasma concentrations of phenylalanine that then cross the blood-brain barrier. Plasma phenylalanine rises to 80-120 mmol/l after a protein meal such as a glass of the “natural substance” milk, about the same as after a dose of 34 mg aspartame per kg body weight (about 28 canned drinks sweetened with aspartame consumed at once); current consumption data show that average daily intake is less than 1% of this and maximum intake less than 10%.
Briffa thinks that aspartame metabolism produces methanol toxicity. According to the US Food and Drug Administration, to cause toxicity in humans, 200-500 mg methanol per kg body weight is needed to produce sufficient amounts of its metabolite, formate (federal register 1984). This corresponds to drinking 600-1700 cans of diet soft drink at once, an amount not achieved after a dose of 200 mg aspartame per kg body weight.
It is also worth noting that studies in children show that sugary drinks make them fatter than artificially sweetened drinks, though the evidence in adults is mixed (perhaps because of confounding as people already concerned about weight may tend to drink lower calorie drinks confusing the direction of cause and effect).
So, overall, there is no convincing reason to suppose that diet drinks sweetened with aspartame are bad for you, especially when compared to the empty calories of sugary drinks which have plenty of bad effects, especially in children.
Update
There have been several low quality studies suggesting that aspartame containing drinks don't have the expected effects on obesity (they don't have any calories, so you might think they ought to help compared to sugary drinks).
But a better quality recent study (“Consumption of sweet beverages and type 2 diabetes incidence in European adults: results from EPIC-InterAct”) has looked at some of the implications of sugary drinks on long term health and has found a significant association with Type 2 diabetes.
The summary of the paper claims:
Results In adjusted models, one 336 g (12 oz) daily increment
in sugar-sweetened and artificially sweetened soft drink
consumption was associated with HRs for type 2 diabetes of
1.22 (95% CI 1.09, 1.38) and 1.52 (95% CI 1.26, 1.83),
respectively. After further adjustment for energy intake and
BMI, the association of sugar-sweetened soft drinks with type
2 diabetes persisted (HR 1.18, 95% CI 1.06, 1.32), but the
association of artificially sweetened soft drinks became
statistically not significant (HR 1.11, 95% CI 0.95, 1.31).
Juice and nectar consumption was not associated with type 2
diabetes incidence.
Conclusions/interpretation This study corroborates the
association between increased incidence of type 2 diabetes
and high consumption of sugar-sweetened soft drinks in
European adults.
The lack of significance of the effect in artificially sweetened drinks after adjustment is noteworthy as it suggests that one reason why other studies have not seen the effect on weight is that they did suffer from confounding caused, probably, because the already fat are more likely to take diet drinks. This study concludes that, for a given group, taking too much sugary drink is clearly bad for you.