Well the new browser on Win 10 (Project Spartan) is definitely much faster than IE on any platform.
As for it being faster than Win 8.1 , my laptop boots faster into Win 10 than Win 8.1 (both using the fast/hibernate booting effect). The rest of the performance seems similar BUT, since Win 10 no longer have this "charms" and "metro screen" it feels alot snappier when using Metro Apps.
Simple example, i use Plex and for the viewer i use the Plex Metro App. In Win 8.1 you have to go to that tile screen and run it there and then constantly have to wave your mouse in some dark corner to get back to the desktop (top left ) and right side to get to "search" etc.
In Win 10 all that stuff is gone, the Tile/Metro App sits on the Start Menu and opens like a normal app on the desktop (you just maximise/minimise it). Search is also on the taskbar, so no more charms in the right/top/corners nonsense.
So that alone makes Win 10 feel faster because i'm clicking/scrolling less and i'm not constantly switching between metro/desktop or trying to trigger charms.
Now of course, if you weren't using any Metro/Charms to begin with, and only used services running in the background / desktop apps running full screen, i guess you might not notice that much.