There's a rather frustrating experience when navigating between Stack Overflow and other SE sites with the new layout/theme. Now that the new theme is live on Software Engineering, I have some side-by-side screenshots showing the differences between the two sites. Switching between the sites, which are supposed to have the same style of theme, is not as easy as it should be.
This shows what you see when you visit the site's home page.
The first thing that is apparent is the misalignment of...well...just about everything. On SE Network sites, the logo is above the pane that displays the content. SO has the logo in the top bar. By shifting the logo location, everything is shifted lower on sites in the SE network. Even if the windows are scrolled to the same location (such as the top of the page), everything will be offset. I'd like to see the SO logo moved to the same place as the logo of the other sites on the network with the top bar getting the Stack Exchange network logo or the Stack Exchange network logo being replaced with the site's logo.
The content of the sidebar is also pretty apparent. Stack Overflow does have some features that SE Network sites don't have - Teams and Jobs, primarily. The order of the sidebar is just different, though. On Stack Overflow, the links in the sidebar should be (in order) Home, Questions, Tags, Users, and Jobs. On Stack Overflow, under Questions (and likely indented), is where I would recommend that links to Teams go. Also notice that Unanswered is missing from Stack Overflow, but I suspect that this has to do with the question filtering that is being tested there. When that rolls out to all sites, I would also expect it to go away from SE network sites.
The implementation of Teams is something to consider. As far as I can tell, there's no way to disable it from showing up on the homepage by default. This may be a feature-request, but it's one related to the user experience once someone belongs to a Team. Depending on how the person uses Stack Overflow and what the nature of the team is, seeing Team questions in your face whenever you visit the site is not always what is desired. Personally, when I visit Stack Overflow, I'd like to see only public questions by default. Having the ability to search across the Teams I'm in and see if a Team has new activity (the red dot in the sidebar) is definitely useful, though.
In all of the Question views, the questions take up a lot of vertical space because of the text under them. On Stack Overflow, the only way to see a list of questions without that text is on the Home view, but that also brings in the list of Team questions. On both Stack Overflow and SE Network sites, the page with the advanced filtering requires you to view the beginning of the question text. This feels like wasted horizontal space - show me more question titles and tags, since that's what I typically use to decide if I want to click on a question to see if I can try to answer it.
I think here, some of the other differences will go away once the advanced filtering stuff is rolled out across the network. I hope that's relatively soon. The alignment issue that I mentioned with the homepage is probably the biggest problem when changing between tabs.
Overall, it seems like the UX issues center around not considering people who use multiple sites on the network in tabs. I have a set of sites that I consider my professional base that I frequently have open in a window at work - Stack Overflow, Software Engineering, Project Management, SQA, and The Workplace. Once all of these sites are upgraded to the new theme, I should be able to seamlessly switch tabs and not have the controls jump around the page when I'm scrolled to the top of the viewport.