I have an AMD E-350, use VLC as a video player, and it drags playing 720p unless I dial down the quality settings. I have not tried 1080p.
That said, you may have better luck with a beefier APU of the 65 W variety. Because VLC will bypass / ignore most of the GPU capability, resorting to the CPU.
The central problem with AMD's low wattage offerings is that many video players fail to make optimal use of ATI's GPU. The only one that claims to make good use of it is XBMC, but I have not been able to get XBMC to run without crashing on my PC, so I use VLC.
I tried installing OpenElec too, and after killing a morning and an afternoon and a USB stick, that did not work.
If you intend to use Linux, I do not recommend the low wattage AMD offerings due to the problems you will encounter trying to get them to play HD video content in Linux. At least consider the Intel 35 W g630t's using socket LGA 1155.
I had a weird problem with one of my ASUS E35M1-M's where it ate a keyboard, a mouse, and a USB stick. Got hungry one morning I guess. Needless to say I went to the ASUS web site and found updates for the BIOS and under the release notes: "Fix for USB device compatibility." I'll say, if you define incompatibility as digestion of USB devices. $30 worth of destroyed USB devices was a hefty hidden cost for these boards.
Not an AMD fan anymore. I don't think AMD gains anything from its merger with ATI.
My desktop runs 64-bit Linux Mint XFCE, my htpc runs 64-bit Linux Mint Xfce, my secondary htpc runs 64-bit Xubuntu, my answering machine runs 64-bit windows 7, my laptop runs 64-bit Xubuntu.