My recommendation, if feasible, would be to purchase a HDMI cable that would go from the Roku to the HD TV. (I am assuming that your HD TV understands at least 720p.) A friend told me that if you are purchasing a reasonably-length HDMI cable (3 to 10 feet), just go with any of the *mart stores (bi-mart, wal-mart) and buy a reasonably-priced cable. When the cable is purchased and hooked up, you can use the HDMI input on your TV to receive the signal from the Roku. If you see the Roku channel menu, go into settings -> Display type, and select HDTV.
I have the original model N1000 Roku "Netflix Player" (yes, my invoice calls it a "Netflix Player"). I was driving an older style TV for a year or so using the composite output because my TV understood only 480i. (Composite output is always 480i.)
When I purchased my HD TV, the next day I purchased a HDMI cable, told the Roku the display type was HD TV, the Roku rebooted, and ever since my TV has been happy with the signal from the Roku. As per HDnation, I changed my TV picture size for the Roku HDMI connection (and later for the blu-ray HDMI connection) to "Screen Fit", which on my TV means the signal will match the size of the screen, whereas its "16:9" picture size overscans (about 10% of the picture is lost outside of the viewable area).
Anyway, with the Roku connected via HDMI to the HD TV, the Roku display mode set to "HD TV", most of the Netflix content makes maximum use of the HD TV (black bars on the side for the old style 4:3 aspect ratio for TV and made-for-TV movies up to just a few years ago; use the full screen for most shows that came out in the past couple of years; but still black bars at top and bottom for panoramic / "vistavision" movies but those aren't as big as they were on the old TV). In fact, I was surprised how well the Roku normally maximizes the use of the HD TV screen without having to resort to chopping off part of the image.
The same seems to be true with my blu-ray player, though I had come across maybe three discs in the past year where the coding on the DVD wasn't sufficient to optimize screen use and ended up with black bars all the way around the picture. Most recently this happened with The Wiz, the blu-ray player matted on all four sides in black. Fortunately, my old DVD player is still hooked up via composite cables and my TV offers more zoom options with composite ports than it does with HDMI ports, so I was able to use a zoom setting that was close, though not as good as when the blu-ray player can both zoom and upscale.
I don't have my HD TV hooked to cable so I can't comment about that except to say that it seems that there seems to be a variety of resolutions used and if a movie is shown on a channel that has only 480 lines and it is shown in widescreen, it wouldn't surprise me if it appears to be completely matted on a HD TV.