That is an excellent question!
No, makes no difference as far as hardware. Energy efficient hardware is just that. The main point of this post is that the hardware is energy efficient AND works with Linux. All of the hardware will work 'out of the box' with a Ubuntu OS. Buy a machine off the shelf and that is DEFINITELY not a guarantee.
If you were to build and energy efficient Windows box, you wouldn't need to be so specific about hardware. The deceptive thing is, of course, that hardware often comes with 'Window & Mac ready' and all that guff, but not Linux ready. Generally, things work just fine with Linux also but best to be careful. You don't want to fork out for a top of the range vid card only to find you have spent two months trying to get the thing to work.
If you want to run Linux and you're building a machine to do it, best to do your research rather than find yourself up s**t creek without a paddle.
Glad you liked the post! It is about time I updated it I think cos things move pretty quick in the world of technology and some of this is outdated. (LED monitors are MUCH more energy efficient that even LCD).