Turns out the trick is super super simple: It's not the sugar; it's the salt. It's on the label.
The soda brands that have been differentiating their cane sugar products, such as the various "throwback" promotional drinks or "Mexican Coke" all have measurably more salt in the cane sugar versions which tends to enhance the flavors for all the same reasons that salt does that in every other food. If you want your corn syrup american coke to have that south of the border $8 imported flair, put about half a pinch of salt in it. It will taste the same, except you won't get to drink it out of the tall glass bottle.