Doubt it.
The Mini idles in a few watts or less and has a max TDP of something like 45 watts. Plus if its semi recent it should support mavericks which will further reduce power consumption, will look less cluttered, etc.
But to be honest I wouldn't/don't even use a Mini. AppleTV, stream from some other machine over WIFI and leave the devices with fans and heat generation in another room away from your home theatre.
I've done the "old retired machine as a HTPC" thing a few times before and it just means you have a power hungry noisy hot machine that takes up a lot of space, looks unsightly and doesn't have a remote.
*shrug*
Apple says it's 85W and it stresses when running 1080p - probably around 60W or 70W. The MP1,1 with one CPU, the 5870, and two 2GB DIMMs would be about 60W when playing 1080P video. So, yeah, close to the same or the MP1,1 might be a little less.