Pros

Very private browser. Browsing History is kept on device instead of the device. When it is kept on device, it is in an encrypted folder that no one even anyone on the Vivaldi Team can see it.
Android version is touted to be the best experience on Android. We do not have an android to test to confirm/deny this.
Includes a "quick commands" feature for you to do all of the things you may need to use several mouse clicks for.
Tab tiling is great for viewing several tabs simultaneously.

Cons

Updates are slow to come or don't come frequently enough to existing features. New features keep getting added without polishing the ones that are already there.
Browsing around the UI is slower than other browsers. Lots of lag compared to others when clicking on menus and using commands when using hardware acceleration though the UI is still slower with it off.
Ad-blocking is not very good in the brwoser. Brave has better built-in ad-blocking than Vivaldi.
Picture-in-Picture may or may not work for no good reason.