So yeah, I was wondering.

Will the questing in enemy territory post 50 also give us access to new dungeons? Or are all factions sharing the same dungeons perhaps?

This would make a huge difference, and effectively mean that you had tons of dungeons to do.

I sure hope I can run into enemy zones for dungeons. I miss that from WoW.

See this article.

http://massively.joystiq.com/2013/03/19/the-elder-scrolls-online-interview-paul-sage/

It doesn't specifically address your question but it does say there are separate level 50 versions of most dungeons

Wouldn't really make sense from a value-for-money perspective to let players into those zones but deny them access to the dungeons.