Beyond the sweetness difference, Classic Coke has a lot more bite. It almost hurts during the first sip of a freshly opened can. Obvious if you are aware of it.
Is that why I hate plastic bottle soda? I've always chalked it up to some sort of either: (a) Taste taint from the container, where whatever they line cans with is better than the PET of the bottle, or (b) The warmer container temperature due to plastic not conducting heat as well as aluminum, causing me to think that the drink inside is warmer. (In other words, psychological issues while drinking from the plastic bottle)
When I was a kid, the absolute best was those 16oz. glass bottles with the polystyrene labels[0]. Somehow that Pepsi was colder than ice and more refreshing than any other version.
I think it is because the plastic container just isn't as strong, so they reduce the carbolic acid content. The cans are stronger, and the glass bottles the strongest.
In any case, I abandoned my Coca-Cola habit about 10 years ago to improve my health. It took about a year to get over the craving for it. I don't miss it anymore.