In the Edge browser, the UI is confusing. Coming from another browser, you might think the book means "bookmarks." Old versions of IE trained people that the star button displays Favorites and the star with the little "+" is for adding the current site to Favorites. Well, there's no "+" on the star button, so it's a bit confusing when it doesn't display your Favorites and just shows the add-to-Favorites dialog. I'll probably never use the Web Note feature, but it always has a button at the top, occupying screen space. The Share button shows the wrong icon for Mail: A rolodex or calendar instead of an envelope. How does that happen?!
The browser UI that impress me the most: mobile Safari on iOS.
16:9 monitors are the norm now. That's great for immersive movies and games, but horrible for reading and working. It's important to minimize the browser UI to free-up as much vertical space as possible for web content. Even on a 4:3 iPad, it's refreshing that the browser can be configured to have far less UI "chrome" and nearly all of the screen space is used to display web content.
I disabled the tab bar in mobile Safari and never looked back. The entire browser UI is consolidated into a single row. Just a tiny strip. On iPad, that strip shrinks to almost nothing as I scroll down. On my iPhone, it disappears entirely while scrolling down. Who needs a bookmarks bar or Favorites bar? Just tap the address bar (almost anywhere along the top of the screen) and bookmarks appear below it. Who Needs a search-in-page button? Start typing in the address bar and the search-in-page option appears below (already showing how many instances appear). Other options like "request desktop site," bookmark current page, reading list, etc are consolidated into the address bar. I absolutely love it. Wasting screen space on an entire horizontal bar just for tabs is pointless when you can have a single button that zooms-out to show all the pages you have open, automatically grouped by site. Even re-opening a closed page can be done intuitively with the minimalistic UI (tap-and-hold on the "+"). Tab and hold on the "<" to list the whole back buffer and jump back as far as you want.
My main problem with Safari in OSX Yosemite / El Capitan is that you can't disable the tab bar. The browser looks perfect until I open a second page.
Why can't I click-and-hold the back button in Edge or click-and-drag-downward to view the whole back buffer? I thought all the browsers worked that way now?
In Edge, I can't right-click a tab and hit "c" to close anymore. That's programmed productivity behavior for me. Sometimes, you can't middle-click (laptop trackpad) and the same shortcut works to close almost any window (right-click the title bar or taskbar button and tap "c" to close).
I'm going to be submitting a lot of feedback on Edge. I doubt it will lead to anything though.