Yes, if your TV screen is large (it sounds like it is), then composite is going to look a little blurry (especially on text, as mentioned earlier). BTW, if you want to stretch or zoom the composite output, you should be able to do that with your TV. Switch to the composite input, then there should be an "aspect" control on your TV's remote or menu.
As for your HDMI not looking right, I'd start by removing the XBox from the chain and temporarily connecting the HW directly to the TV via HDMI. (You'll add the XBox back to the chain later.)
Set your HW's resolution to the value nearest your TV's "native" resolution. Use 1080p or 1080i if your TV's screen has at least that many lines; if it has fewer, use 720p. At this point, the HW output should look very close to your TV's tuner.
Now disconnect the HW, connect the XBox, and set your XBox's output resolution to the same value as the HW. Finally, hook the HW up to the XBox. Hopefully, everything will be OK now.
What we're trying to do here is avoid rescaling the image more than necessary. We want the HW to scale the image to the TV screen's resolution, or at least as close as possible, then stay the same resolution going through the XBox, then hopefully the TV won't have to rescale it again, or at least not by a noticeable amount.