The redesign in Opera One looks good but needs major work to improve its UX.
Biggest issue: the border around the webpage - worst UI decision I've ever seen in a desktop browser
I'm using a very standard setup (one 24 inch 1080p screen) and there's a 4px border around the web page. That means 8px of screen real estate wasted horizontally and 8px vertically. With a maximized window, the loss of space is noticeable compared to all other browsers and the screen feels smaller for no good reason. When the browser window is not maximized (ie. smaller window), it's even more obvious. And when you have multiple browser windows visible on your screen or pop ups open those borders are everywhere. The new rounded corners steal even more screen space.
Scrollbar usability killed
This has been mentioned by many other people, you can't reach the scrollbar anymore by dragging your mouse cursor to the right of the screen and just clicking. Also, the rounded corners cover part of the up/down buttons making it harder to click on them.
Then there are many minor issues. Here are some:
No hamburger icon in the standard location (rightmost position of the navigation bar)
There's a reason all other browsers have the hamburger icon there, it's an easy location to find visually and reach with the mouse. Opera 100 puts an icon here that most people won't find useful (extensions).
When lots of tabs are open (using the full width of the tab area), the active one gets resized
Again something that looks good but affects usability when you're switching between tabs with the mouse. All other modern browsers don't have this issue.
Big gap (8px in my screen) above the tabs
In Opera One, when you have a maximized window you can drag the mouse pointer to the very top of the screen and click on a tab (which is good). However the gap is so large that it's not intuitive to assume that a click on the gap will trigger a click on the corresponding tab.
Other browsers deal with this by making the tabs reach the top of the screen or they use a tiny margin, certainly not 8px.