By using the S-video cable, you are using the digital comb filter in the Dish STB.
By using the Composite cables you are using the digital comb filter in the GWIII.
The GWIII is upscaling both connection types to 480p using the DRC circuitry as I understand it.
Unless you can prove (by eyeballing it) that the S-Video looks better than the Composite, the composite my be the way to go.
I am using the S-Video out of a Zenith HD SAT520 (4 Line Y/C Digital Comb Filter) and it looks better to me, than the Composite connection which uses the GWIII comb filter. However, I don't know if the SAT520 is 10bit so there may be a sacrifice on the gray scale....
Edit: Giving credit where credit is due...I wouldn't have been able to answer that question 6 months ago, but UMR is very knowledgeable and has taught us/me quite a bit about these sets.
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