For me, it's both.
Nesting is helpful as a visual history indicator and a quick way to prune unused tabs that were opened closely in time. Great when you're doing a quick research.
The vertical display helps locating tabs by its title and in general, narrower text on a page is easier to read. (Most screens nowadays are widescreen. Some blogs even overcompensate for this by having huge margins and even huge ads on the sidebar, but that's another story.)