It's not a battle if they're being dragged into it. Browser vendors are playing catch up with web developers, and they're running out of breath. All it takes is Facebook or Zynga to standardize on, say, Webkit + Unity3D for the rest to lose. That's not a battle, that's running for your life.
There are simply far too many viable options waiting on standby, and eager to step in, for this to be a clash of the titans. The source trees of your average modern browsers are all identical, with the same people working behind the scenes. From a brief experience, I can tell you that Tamarin and Dalvik teams are stealing glances at each other's scantrons ;-)
