What I've learned trying to analyse my preference for vertical tabs is that it's not so much about saving horizontal space vs vertical space. It's more just about showing more information on screen before needing to scroll.
With regular horizontal tabs you either squeeze all tabs to fit the window width, in which case you stop being able to read page titles at some point. Or you have a horizontal scroll on the tab bar which also means you can only read so many titles on screen (probably fewer) before needing to scroll.
The vertical tabs switch this up by being able to show a larger number of tab titles before you have to scroll down. Of course this depends on the width of your vertical tab sidebar but having word wrap or configurable height on horizontal tab bars isn't ever presented as an option so can't compare.
Another clue to understanding my preference was when I realised I actually really like being able to have multiple rows of horizontal tabs vs a horizontally scrolling tab bar. So I think it just came down to the density of information visually available before having to do any scrolling.
I do think it all just comes down to personal preferences and muscle memory and individual use cases (for example, some people like having 50+ tabs open, others don't). So I am very hesitant to call one approach better. I just don't understand why we can't have both options more available everywhere.
