The demand for Caffeine-Free Diet Coke should be more elastic than the demand for soda in general. This is because there are more substitutes for this particular kind of soda than there are for soda in general.
If the price of Caffeine-Free Diet Coke goes up, consumers can choose many other kinds of soda. They can try Caffeine-Free Diet Pepsi or they can try Diet Coke with caffeine, for example. However, if the price of soda in general goes up, there are fewer choices. A person who likes soda is less likely to want to switch to drinking water or drinking fruit juice. These are not close substitutes for soda.
An analogous situation is discussed in this link. It tells us that
The demand for a specific model automobile would likely be highly elastic, because there are so many substitutes.
In the case of soda, Caffeine-Free Diet Coke is like a “specific model automobile” and will have highly elastic demand compared to soda as a whole.