1) HD6800 and 6900 series fixed a
texture transition/filtering problem of the HD5800 series. Although this affected very few games (such as Half Life 2 or TrackMania 2), it's worth noting.
2) The Universal Video Decoder (UVD) was upgraded to version 3, bringing full decode support for MPEG-2, MPEG-4 ASP, and H.264 MVC (packed frame video for 3D movies).
Xbitlabs also shares the view that UVD 3.0 isn't much different from UVD 2.0:
UVD 3.0 offers hardware acceleration for decoding video in a number of formats (DivX/XviD, MPEG2-HD, MPEG4-AVC, MPEG4-MVC, WMV-HD, VC-1, Adobe Flash 10.1, etc.) and supports bitstreaming of many audio formats via HDMI. It can also do hardware post-processing of SD and HD video. In other words, UVD 3.0 is not much different from the previous video engine.
In particular, the
video quality scores for DVDs and Blu-Ray between an HD6850 and HD5750 (identical UVD to 5850) are pretty much the same. The biggest difference is the CPU load when playing higher quality content.
3) The 6800 series also introduced support for HDMI 1.4a and support for color correction in linear space. HDMI 1.4a support is fairly straightforward: the 6000 series can drive 3D televisions in either the 1080p24 or 720p60 3D modes. Meanwhile support for color correction in linear space allows AMD to offer accurate color correction for wide gamut monitors; previously there was a loss of accuracy as color correction had to be applied in the gamma color space, which is only meant for use for display purposes. This is particularly important for integrating wide gamut monitors in to traditional gamut workflows, as sRGB is misinterpreted on a wide gamut monitor without color correction.
4)
Like its predecessors, the Radeon HD 6800 series supports Protected Audio Path and can bitstream 7.1 audio (192 kHz/24 bits per sample) with a bitrate up to 6.144 Mbps in AC3, DTS, Dolby True HD, DTS HD/DTS HD Master Audio, LPCM (Linear Pulse Code Modulation) and other advanced formats via HDMI 1.4a for further decoding on an external receiver.
The biggest advantages of 6850 series are Eyefinity for more than 3 screens and lower power consumption. I think some HD5850s supported more than 3 displays but they were labelled Eyefinity 6 version, while I am sure in theory you can run more than 3 displays on a single 6850. However, the counter side is that your HD5850 probably has 2x DVI ports and they can drive 2x 2560x1600 displays using DVI, something that's not possible on a 6850 without an HDMI-to-DVI or Display Port adapter.
However, I can't see any advantages that HD6850 has for an HTPC in terms of sound or non-3D image quality. So I wouldn't particularly worry about it and keep what is in your case a quieter and slightly faster 5850.