Sugar is latest public enemy but there have recently been several studies of, and popular press reactions to, the idea that artificial substitutes for sugar may be worse for you than sugar. Two of these medical study reports are 1 and 2.

In the first reference researchers used the famous frequently studied community-based Framingham Heart Study Offspring cohort. They watched 2888 participants aged >45 years for  stroke occurrences (mean age 62 years; 45% men) and 1484 participants aged >60 years for dementia (mean age 69 years; 46% men). They have been following these worthy volunteers since 1991 and had been asking them things about what they ate and drank along the way.  There were 97 cases of stroke and 81 cases of dementia (63 consistent with Alzheimer’s disease) during the observation period. After adjusting for age, sex, education (for analysis of dementia), caloric intake, diet quality, physical activity, and smoking, they found that higher recent and higher cumulative intake of artificially sweetened soft drinks were associated with a three times increased risk of ischemic stroke, all-cause dementia, and Alzheimer’s disease dementia. Sugar-sweetened beverages were not associated with stroke or dementia.
The second study was an analysis of multiple studies. These authors found 7 trials (1003 participants; median follow-up 6 mo) and 30 cohort studies (405 907 participants; median follow-up 10 yr). In these studies non-nutritive sweeteners had no significant effect on weight and shape or a modest increase in BMI (mean correlation 0.05, 95% CI 0.03 to 0.06; I2 0%; 21 256 participants). Data from these studies showed no consistent effects of non-nutritive sweeteners on other measures of body composition and reported no further secondary outcomes. In the cohort studies, consumption of non-nutritive sweeteners was associated with increases in weight and waist circumference, and higher incidence of obesity, hypertension, metabolic syndrome, type 2 diabetes and cardiovascular events.
But these studies except for the very short term trials are observational and cannot prove causation. There are lots of things that make people who drink diet soda different from you and me. Things that may not be considered and controlled for in an observational study. These people are special. I know some of them. 
If there was some sort of causation connection what could it be? Some conjecture that fake sugar changes the bacteria populations in your intestines. Or somehow maybe fooling you brain and body into thinking it's getting sweet stuff does other bad things. 
I think drinking diet pop is silly.

1. Pase MP et al. Sugar- and Artificially Sweetened Beverages and the Risks of Incident Stroke and Dementia A Prospective Cohort Study. Stroke. 2017;STROKEAHA.116.016027. https://doi.org/10.1161/STROKEAHA.116.016027
2. Azad MB. et al. Nonnutritive sweeteners and cardiometabolic health: a systematic review and meta-analysis of randomized controlled trials and prospective cohort studies. CMAJ  2017; 189 (28): doi: 10.1503/cmaj.161390