With a properly calibrated input on the TV when using component video, you should not see a significant difference between HDMI and CV, if the CV connection is directly to the TV. You obviously cannot go "through" the DVD recorder since then you're limited to 480i on the CV connection there and will degrade the HD signal.
See the following thread on HDMI issues.
And the following on proper TV Setup
There is no other firmware available and you cannot use both HD connections at the same time. Sometimes people can use a workaround to get it working for what their needs are, but not for simultaneous functioning I believe. See the following previous similar discussion:
For times that you wish to record while watching, you could use the S-video connection to the DVD recorder, which should not cause the problem with the copy protection message. Since consumer DVD recorders are limited to 480i on CV, the S-video should not be a significant step down under those circumstances.