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.
Diet Caffeine-Free Coke has more elastic demand than soda in general because it is a specialty product, even though there are similar products that are competing against it. Soda, in general, has few or no substitutes. In this example, a change in price in soda will impact consumers with the inelastic demand because of limited acceptable substitutes.
If the price of this caffeine Coca-Cola product increases significantly, consumers may decide to buy something else, and they can. They can choose another company's diet caffeine-free cola product, such as Caffeine-Free Diet Pepsi. Therefore, Caffeine-Free Diet Coke may experience a loss of sales because consumers may switch to a substitute less expensive diet-caffeine brand name or to a private-label substitute. This defines price elasticity. Therefore, the specialty, niche soda has more price elasticity, also said as high elastic demand.
However, with the general soda market, if the overall price of all sodas were to go up across the soda market, there would be few or no substitutes for soda, so the entire market would experience price inelasticty and consumers would pay the higher price across all soda brands because of no substitutes. The result is that the specialty niche Diet Caffeine-Free Coke has more price elasticity (consumers have more price and product options because of the abundance of substitutes).