According to the Toyota Prius website, Toyota Prius Hybrid - 2010 Models: Prius II, Prius III, Prius IV, Prius V the II does not come with bluetooth. I believe you can get it as a dealer add-on though.
I believe you can get the Blu Logic bluetooth connection as a dealer installed option. My 2010 has it but not the JBL system. The Blu Logic works very well with the base stereo.
Does it have all of the capabilities of the bluetooth that comes with the factory installed Bluetooth that comes with the III?
Mine, came factory installed but not integrated into the steering wheel. In fact the dealer had 2 in stock. The button is located on the right side of the steering column, a bit inconvenient. As to the function compared to the III, I am not familiar with it.
I too can vouch that the dealer-added BT works flawless (even when driving). As pointed out earlier, the location is an inconvenience. I didnt mind paying extra $150 for that feature (compared to $900 for III).