Exactly what batman said. The only difference is that the HD PVR is a device, and the BMiP is a card that you install in your pc, and that you can play in 1080P(BMiP) not in 1080i(PVR) witch is basically the same thing.
And yes, you CAN play in HD while recording.
I did not buy the BMiP and got the PVR instead because I got a mac and, yeah.
But if you are actually that kind of guy who has no problem with installing shit in your pc and raging, get the BMiP, I recomand you the PVR tho.
Your choice.
/v/