I have the Hauppauge 1600, and it works like a charm. The drivers now support 64-bit with 4GB or more of RAM (I have 6GB), and it works wonderfully with Media Center. Just make sure you get a remote from Microsoft, as the one that comes with it doesn't work 100% of the time (at least for me).
I have the Hauppauge 1800 with Vista Ultimate 64 and it works well, also got 8 gig of RAM. As for the remote, you'll definitely need a Microsoft one if you're receiving your signal through a cable box. There is no work around this sadly. If your cable is directly plugged into you're computer than it's not necessary. Depending on your set up, a remote might not even be needed. I don't use one since I am recording and watching on my computer monitor.
I also use the Hauppauge 1600 with 64-bit Vista Ultimate and 4GB of RAM. My setup works like a charm including Media Center and the included remote. I didn't even get the MCE edition. My HD content is OTA which may make a difference.
If you use 3rd party software like Myth TV you tend to be better off for both companies.
I'm just about to add a Hauppauge 1500 to the ATI650 I already have. I MO it's more about personal preference than other things, and to me form factor is more important since both companies do a real good job.
And as for random noman's post, both ATi and Hauppauge have their issues, and both struggled with Vista early on (more of a vista issue than ATi of Hauppauge's), however they are both much better than the other options out there and have improved alot over the past year.