The Roku 2 has the same speed as the Roku 3. AFAIK, Both of these devices are fast. They do not lag unlike the older Roku devices. You lose out on some features that the Roku 3 has, but they are both equally fast devices. I have the Roku 3 and it's a very fast UI.
Roku is also offering 2 months of HBO Now but the terms says the device must be activated starting July 24, 2016.