Consumer Action Line in my local newspaper just ran a comparison between these two 'black' boxes. The TIVO won hands down. There have been many reported problems with the HR20 - everything from flat out failures to missed recordings. Get the TIVO.
The HR20 is a complicated new box and the cornerstone of D* HD strategy. Neither the TiVo S3 or the HR20 are perfect yet. Look at the wider picture; consider total cost over a couple of years and look what HD programming is promised by the service operator. With both options you could be committing yourself to a 2-3 year contract.
Also consider a monthly lease from your cable company of their own HD DVR if they offer one. If they do not tie you into a long service contract then you can postpone your decision for a few months until the S3 and HR20 falls in price and any issues have been worked out.
I think that the Tivo Series 3 is not compatible with D*V, can get the HR20 for 299 plus they will put new dish 5 LNb up for free, already have hd premier package so no monthly fee for dvr use. 1 yr commit. Is the Tivo 3 Series m-peg 2 ?. I no the HR20 is m-peg 4.