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.
When I say copy an application, I mean that I actually copied an entire application in the New UX - 1. I went to the Apps area in the New UX where you can see a list of applications you have access to 2. I clicked the ellipsis to the right of the application name 3. Selected Duplicate App.
When I say secondary table, I mean that I had set up a table in the Additional Insights section of a few worksheet type dashboard in the application (the one I copied) and selected the option to Set As Open by Default - which give you a "secondary table" open below the primary table as soon as you open the worksheet.
What I found was that after copying the application all of my tables that had been Set As Open by Default no longer had that setting selected. This caused me to have to go back into each worksheet and redo that setting. Let me know if you're able to recreate the issue! Much appreciated!