Living Room PC

IMO, get the Hauppauge 1800.

The 1600 is good and a minimum level of support for QAM using clear cable, but the 1800 seems to have better support for Media Centre and a little better support. There are other IHVs out there like ATi, but I would go for Hauppauge jut for the consistency of hardware support and their slightly more secure future (ATi's a bit of a question mark after selling alot of their division to Broadcom).

What OS are you using? You may find even with the best support in the biz, it's still a pain setting up HD Tuner cards under MCE, and especially under Vista's MC app. Be prepared to go into the forums of whichever company you end up buying from, other people's experience in getting past the various barriers to installation (thanks to DRM) is very helpful. I had alot of trouble with the ATi TV Wonder 650 USB and only figured it out after reading a similar solution to a 600 series problem.

The output will be handled by the graphics card, the 1080P depends on the source material.

IIRC no un-encrypted cable is 1080P and no OTA is 1080P, so it mat be a 1080P output, but of a 1080i/720P signal input.
But the Hauppauges do support 1080i input, displaying that 1080i to your TV will involve all the DRM fun of Windows and hardware support of your graphics card. MCE's drivers are also sketchy, so you're going to have to check with your graphics card maker as to the output support.