what is the chemical difference between diet soda and regular soda?
Regular soda contains sugar, high-fructose corn syrup, fruit juice, or a combination of these. Diet soda, on the other hand, contains artificial sweeteners meant to reduce the caloric content of the soda. A popular artificial sweetener found in diet sodas is aspartame. Aspartame is one of the most commonly used sweeteners today, sold under various brands such as “Equal” and “Nutrasweet”. Aspartame is meant to mimic the taste of natural sugar. But since aspartame is about 200 times sweeter than sugar, much less of it can be used to provide the same level of sweetness, and this can help lower the caloric content of soda. 
does regular soda lead to weight gain?
There is constant debate about high fructose corn syrup and whether it has a greater effect on weight gain and weight gain-related diseases than other sugar sources. A 2007 study published in Critical Food Reviews and Science Nutrition concluded that contrary to popular belief, high fructose corn-syrup does not lead to exacerbated weight gain in comparison to other sugar sources. 
On the other hand, A 2010 study published by Physiology & Behavior deduced that regular consumption of sugar-sweetened drinks, including soda, could lead to weight gain and an increased risk of developing type II diabetes. However, it is important to note that these risks are applicable mainly when drinking soda leads to excess caloric consumption and the intake of other sources of calories is not restricted in exchange. Research shows that soda is indeed a large contributor to excess sugar intake in the United States. Excess sugar could lead to insulin resistance and impaired beta-cell function, thereby leading to type II diabetes. (Beta cells are pancreatic cells that release insulin in order to regulate blood glucose levels.) 
can diet soda help you lose weight?
A 2014 study published in Obesity investigated the effect of non-nutritive sweetened beverages, which include diet soda, on weight loss. The researchers divided over 300 adults into two groups: One group was asked to drink at least 24 oz of non-nutritive sweetened beverages daily, and the other group was asked to drink at least 24 oz of water daily (and no non-nutritive sweetened beverages). Over 12 weeks, the participants drinking only water lost an average of 9 pounds while the participants allowed to drink diet soda lost an average of 13 pounds. Researchers concluded that this difference in weight loss was probably due to a reduction in hunger levels in the participants allowed to drink diet soda. He concluded that substituting regular soda with diet soda could potentially help those who drink soda regularly to lose weight. 
However, a 2010 study in the Yale Journal of Biology and Medicine found that although artificial sweeteners don’t contain calories, they encourage sugar craving and sugar dependence due to their sweetness. Repeated exposure to a particular flavor increases one’s preference for it. A strong correlation indeed exists between a person’s habitual intake of a flavor and his level of craving for that flavor. 
can diet soda cause cancer?
A 2012 study published by the American Journal of Nutrition evaluated whether the consumption of aspartame and regular soda is associated with the development of hematopoietic cancers (cancers that occur in the cells of blood-forming tissue, such as the bone marrow, or in the cells of the immune system). While findings suggest that aspartame could play a role in triggering certain hematopoietic cancers, more evidence is required to draw concrete conclusions. 
The effect of diet soda on various types of cancer, including non-Hodgkin lymphoma (a cancer that affects the immune system), was also explored by three studies published in the American Journal of Nutrition. While the results shed light on the potentially cancerous effects of soft drinks, more long-term studies need to be conducted in order to provide definite conclusions. 
is there any correlation between diet/regular soda and other diseases/health issues?
A 2010 study in Physiology & Behavior noted that there is emerging evidence for the adverse effects of sugar-sweetened drinks on other metabolic conditions, including hypertension, inflammation, atherogenic dyslipidemia (a metabolic abnormality), hyperuricemia (excess of uric acid in the blood), gout (a form of arthritis), gallstone, and kidney disease.  However, more research is required to confirm the relationship between soda consumption and these diseases.
In addition to weight gain and disease, soda can also cause tooth decay. Soft drinks contain phosphoric acid and sugar which attract bacteria such as lactobacillus and streptococcus that cause dental erosion. While diet soda is sugar-free, it can also cause tooth decay due to its acidity. 
While consuming soda in moderation is okay, it is important not to drink soda (diet or regular) on a daily basis. Opt for natural fruit juices or coconut water instead. However, these drinks have a high sugar content as well, so it is important to primarily drink water.
In terms of whether diet or regular soda is better, it varies on a case by case basis. For example, for an obese person with high sugar levels, drinking diet soda in moderation would potentially be less harmful.
Overall, regular soda and diet soda provide minimal nutritional benefit and increased chances of weight gain, disease, and tooth decay. As with all foods, if one chooses to drink soda, one should keep an eye out for changes in health.