I've heard Steve talk a few times about his Tab issues and his preference for Vertical Tabs - which I share. So a while ago, I tried out Vivaldi, and almost immediately made the switch from FireFox!
Since this thread is pretty old, and Vivaldi is actively developed, the preceding posts don't really mention a some of its newer features, so here's a screen shot with a bit of explanatory text. (Pardon the blurred bits - Some things are private!)
First, on the left, the tabs. You can now have Tab Groups with a second layer of tabs in them. As shown, each Tab Group displays the number of tabs it contains, and as you can see, when you hover your mouse over a group, you get a preview of the tabs within it. You can click directly on the thumbnails as well.
Almost all the Tab functions, re-arranging, grouping, etc. can be accomplished with drag/drop.
My tabs are fairly complex, so here's the lineup. Pinned tabs automatically go to the top, though you can rearrange them within the section with drag/drop. I created a web page that's basically blank and named with double-lines. I use it to make "divider" tabs and tab groups. So at the bottom of the "pinned" section, you'll see one of those, also "pinned" so it stays up there.
The second section is Tab Groups containing at least one Pinned Tab (you cannot pin a group, but pinning one tab within a group pins the group). I have three of these groups. Then another divider and my "normal" Tab Groups. Note that Tab Groups can be renamed, so I put a colon at the beginning of each and make it all-caps to quickly show it's a group (I started that before the visual "outlining" of groups was added, so it's not really necessary, but still works for me). Below the "Normal" (unpinned) Tab Groups are normal single tabs.
I like to have the second column of tabs locked, so things don't move around and my eyes can find things quickly. It's an option you can activate by clicking on the lock icon at the bottom of the second column. Makes things much easier. If you don't have it locked, then the second level disappears when you're not on a Group.
Another tab function I LOVE is the trash can. Many times some website will open another window with only that site/tab in it. I have Vivaldi set to remember tabs, so if I close the main window, then close the second window, that's what it remembers, so when I re-open Vivaldi, all my tabs are gone! Fortunately, they're in the garbage can, and I can restore them ALL with one click - including placement, pinning and groups.
Vivaldi sync also allows me to "grab" my main browser's tabs in other instances of Vivaldi on other machines. You have to log into your sync account of course, and it's all encrypted. You can see your other Vivaldi instances and how many tabs it has by clicking the cloud icon at the bottom of the 1st row of tabs. I have four machines I use commonly, so this is a huge time-saver as well.
Vivaldi has a lot of other features I love too. For example, the "Panes" on the right. (They're on the left by default, but I find them handier on the right). Each is a "mini browser", and as shown, mine currently has the Speedtest.net site selected. I use this a LOT in troubleshooting, so being able to open and use it with a single click - and while the "main" window is still visible - is a huge help.
Another great feature is the Notes, including the fact that the Notes is a built-in "Pane" for easy access. In the pic, the built-in Notes is the active tab, just to show what it looks like. They also sync across instances of Vivaldi.
One more thing I love, that doesn't get enough mention, is the Bookmarks Bar. I use folders in my bookmarks bar to organize them into cascading "menus". Others browsers have this functionality as well. But Vivaldi had a lovely feature the others don't. When I open one of these folders, I can navigate to the correct sub-folder, and THEN, when I know I'm in the right place, there's an "Add Active Tab" link so I can add the current tab to that folder/subfolder without having to click "Save Bookmark" THEN do the navigation. I find this FAR more intuitive. (Second pic).
Finally, I have to mention the Start Page. I've used many Start Page Add-Ons over the years, and Vivaldi's built-in Start Page blows them all away. It's very easy to use, extremely customizable, and supports folders and custom thumbnails. Here's a quick shot of mine, just to give you an idea. The "Google" and "Vivaldi" items are folders with sub-start-page items in them (which are also customizable):