Unfortunately the offloading requires compatible hardware AND software. For example, the HD series of ATI cards have hardware to do not only decoding of various codecs (VC1, Mpeg4, etc) but also decryption. One of those combined even with a relatively feeble single core 2 ghz CPU is all you need for smooth 1080p HD playback. For this to happen you need ATI's signed drivers and player software capable of talking to said drivers -- this happens only on windows. The drivers and player also need to be properly signed to maintain an encrypted HDCP path all the way from the disk to your eyeballs once HD disks start enforcing encryption.
None of that exists for Linux. Not a single ATI card or onboard chipset is capable of *any* accelerated playback. Not even Mpeg2. This is completely a driver issue. Closed source drivers don't support the functionality AFAIK, and the specs may never be released to let open source drivers do so.
With NV cards, drivers and players you at least get mpeg2 acceleration. This helps, but doesn't solve the entire decode mpeg4 from optical disk problem. The only solution with open source is to have enough CPU oomph to decode the data streams fast enough to generate 1920x1080x60fpsx24bpp or ~370 megabytes/sec of frame buffer data.
On board video of the G690 helps in that respect for Windows by offering support for quite a few codecs, and the 6 and 7 series nvidia onboard chips help a bit on Linux by offloading motion compensation. But even so, you need macho CPUs for the decrypt&decode phase. A mostly CPU solution means 2.6 ghz or so core2 cpu or equivalent is required. You'll get dropped frames and out of sync audio with only an 3800x2. You should be fine with a 5000X2, but ask and see.