I would be wary of spending much on either unit with Boxee being sold to Samsung and support at an end.
Putting that concern aside the Box is still quite usable. They are two very different units however, the Box has far more robust local and streaming playback capabilities and is by far the superior unit. With the demise of the BTV's cloud DVR functions it amounts to little more than a digital tuning box with more limited playback. It may have more playback capabilities than I am unaware of, I don't have one, but early reviews pointed this lack out. My Box still functions pretty well with Boxee+, but no, it can't installed on the BTV. There is also a working port of XBMC that runs on the Box. It's still being sorted out but works. I see the Box for sale used, I got one for $25. That was a lucky buy but I still see them for under $100. Just looking on CL in my area I see one for $60 and a tv dongle for $35. Anyway, the Box is the better unit but I wouldn't shell out the retail bux for a new one, if the Boxee Box server gets shut down the Box will lose online functionality.