I read an interesting article on Shine about diet soda making you fat. They never come out and say it, but it sounds like the aspartame suppresses leptin making you feel hungry when you really aren't. (At least I think that's what Dr. Lustig would say about it!) There are plenty of naysayers in the comments, but I think there is more there than just the correlation between being overweight and drinking diet soda.
The article describes that the researchers observed how the brain reacts to sugar and aspartame. Basically, there's more of a "satisfaction" response from sugar. So, aspartame makes your brain expect that satisfaction, but it doesn't get it, so you want to eat.
One of the basic ideas on the BFC is that artificial sweeteners trigger cravings. Cruise does recommend Stevia, however, because it does not have an impact on blood sugar and therefore does not create cravings. This has been true so far for me, anyway.