Nope, not that I can see.
One of the improvements advertised for Sense 2.1 was more browser windows - at least 9 as I recall.
Other things to note with the Sense browser - whereas the Evo browser would just run slow if you ran it long enough (core leaking) this one will force close (and unlike the Evo 2.2 management, this one gets shuffled out of memory often, but that's likely how I'm using my phone, no big deal).
The other thing I notice with this brower - when you hit the back button, it takes you to a cached copy, not the current page. If you use it to browse this forum as I do, that's a pain in the neck.
Other change - if you go to enter a web address by editing the existing one, the "http://" isn't left behind.
BTW - stock browser tip: In your address bar, enter just this, no http:
about:debug
And then go to Settings. You can turn off Java console and set your UAString to Desktop. Those settings stick between browser sessions. Will screw up sites where you can normally download Android apps (such as iHeartradio) so, you want to remember to switch that back to Android as your needs dictate.