As far as subjective measurements go, it's night and day. Repainting is quicker, pages load faster, content (like images) streams in more quickly onto the screen, and the UI in general pauses less. It helps that they also overhauled the user interface so that it's easier to use, which makes it feel faster even if it actually isn't.
I always speculated that a lot of the random pauses/hangs in the Steam UI were caused by IE, and now I'm fairly certain as most of them are gone in the new one.
I tried using it earlier and it is a lot quicker. The only downside I've noticed is that an individual game sometimes takes up to 5 seconds to load, but I suspect it's my connection rather than the client itself.
I always speculated that a lot of the random pauses/hangs in the Steam UI were caused by IE, and now I'm fairly certain as most of them are gone in the new one.