You should be able to run decent video playback on that system whether it be from Boxee or another program. The performance on either output of the ATI HD2600 should be identical per resolution. That is, you should see the same behavior at on either port given the same output resolution.

Outputting video at higher resolution isn't generally very taxing either, so you won't necessarily experience much more load at 1920x1080 than you would at 1280x720. Example: playing a 640x300 video at either output resolution (full screen or otherwise) should be a cake-walk for that system.

The most taxing aspect of playback is the video decode and that's proportional to the resolution of the video file itself. And of course also depends heavily on the codec used to compress it. If you have assisted hardware decode this is going to help a lot, otherwise it's going to be all CPU. In this case, it also shouldn't matter where you're outputting the video with respect to the ATI card.