The only difference I could think of would be perhaps a reduced chance of fungal issues.
The reasons a lot of people avoid corn are:
Corn is susceptible to a fungus that is toxic to rabbits.
Corn contains a lot of sugar, and starch that is converted into sugar.
So the issues are that you can make your rabbit fat, or you can make it ill or possibly kill it with corn. I would guess that popcorn would be less susceptible to the fungus, just because of how it is stored, but I don't know. Unpopped, I don't know if a rabbit could eat it, as popcorn is much harder than regular corn.
Many, many rabbit feeds contain some amount of corn. I have never seen a rabbit feed myself that did not contain corn. My rabbits have had corn as long as I've had them because of this. Both rabbit chows I've used had corn, and the horse feed I am using now contains it as well.
A lot of people on here mix their own feeds in order to be able to avoid corn altogether, among other reasons.