I just use OpenElec's version of XBMC. It resides on a 16GB SD card. I have a cheap MCE Remote and USB receiver that I use to interact with it.
It plays all my media (mostly 720p or 1080p mkv videos) which is stored on a NAS. I can also stream stuff from any of my Macs or iPhones/iPads to it via AirPlay.
I would only "switch" from my Mac Pro if I was already looking for a new computer. But back on topic (since the OP asked about a Mac Pro 1,1 as a media server):
A Core 2 Duo Mac Mini (which is plenty for a media server... I had one before I got my Mac Pro) will cost you $100 on eBay. Toss in another $200 for 4TB of external storage (maybe less if you shop around) and you're at $300 up front. The cheapest Mac Pro that the OP linked to is $800, and only comes with 250GB of storage.
So not that it much matters the details of the power consumption at that point, but:
The Mac Mini (13W Idle/110W Max) uses less than half of the power of a Mac Pro 1,1 (171W Idle/250W Max. The Mac Mini + the hard drives is still going to be less than half of a Mac Pro.