I very much agree with all the other comments regarding the vertical navigation pane. Having that is one of the big UI *improvements* that I very much like and prefer in the Windows 10 version of the app. I especially dislike how the horizontal pane hides the other tabs in the notebook when going into a section group. I think the vertical tabs are a much more elegant solution, and a better UI.
I also find it very convenient to have the search (and *especially* the "Recent notes") buttons where they are in the Windows 10 app vs. having to switch to the history tab, then click on "Recent edits", then select a time period, and *finally* get some results.
I also quite like the responsive UI in the Windows 10 app - specifically in regards to the content, search, and history buttons - and I like how easy it is to switch to minimal UI (NOT full screen) and back (very minimal mouse movement required) vs. the other app having to go all the way to the right side of the screen to click the double-arrows which also loses the ribbon bar and other UI elements.
One other minor item is that the font size for the sections and pages text in the Windows 10 version is a bit bigger, and I find that easier to read. If there was an option to adjust that, that would be good.
And finally, I use the "Black" theme for office - specifically for Outlook. I find that I generally prefer that for email. BUT - for OneNote that's a different story. I prefer the Light color scheme there. Among other things, it presents font colors and especially highlighting (things I don't need or care about in Outlook) much better than a black background. The fact that the Windows 10 version of the app ISN'T part of the Office suite allows me to use separate color schemes.
I'll add that I'm a HUGE fan of OneNote. I've been using it since the very beginning back in 2003, and as IT Director at the time, I developed training for using it and was a big proponent to other employees at the company where I worked. I use it daily for both work and personal stuff (much more extensively for personal) and I can't see not having it. But I do feel like the overall UI of the Windows 10 version of the app is better in a number of ways than the other version, and I'll be sad if we lose a lot of its features.