The UI design of DT has never felt particularly outdated to me. I personally like its very information dense design although I understand how overwhelming this is for new users.
If there is one UI design I think has a lot to offer in the way of ideas for the next version of DT, it would be Scrivener. Conceptually it has a lot of similar workflows as DT although to a different purpose.
I think Scrivener makes very good use of screen space while still making a lot of information available. To highlight a couple of things I think DT could borrow.
- The multiple pane view is very flexible. It possible for example to have an outline view in each pane, open to different points in the pane, or to flexibly switch between outline, corkboard and document view in either of the panes.
- Flexible metadata for each document in a docked info panel. Custom Metadata, External links, Keywords, Comments etc.
- Better handling of long titles as I noted here : Feature request: More flexible title display.
- The scrivenings display where multiple documents can be viewed together as one continuous document for reading or editing. I am not suggesting that DT should try to replicate all the features of this mode, but a basic version would be useful for those of us who do most of our writing in DT. I also think such a view has a lot of potential as a way of bookmarking pdfs in a more flexible way than any current product allows.
- The collections view for saved searches is very cleverly implemented. I think DT’s smart groups are ultimately a better solution but its worth thinking about
(This is not a criticism of DT, which I love, use everyday and depend upon completely. They are very different products despite their overlap in some areas)
Can’t wait for the next version of DT 
Frederiko