I'm intrigued! When you say copy an application, do you mean copy a page or worksheet; or, did you mean when you upgrade your classic dashboard to New UX? Also, I'm assuming the 'secondary tables' reference is a saved view.
For the first assumption, you shouldn't see any differences in the page copy unless there's a difference in the security. Can you give a step by step approach to what you did? I'd really like to duplicate what you saw.
For the second, basically, only grids and text will transfer from classic to New UX. If you have a lot of customizations, you'll likely have to rebuild your view in New UX.
Check out the New UX Forum, a curated list of New UX topics. This might have been addressed there already. Hope this helps.