Hi Lars,
"You should be able to get the sharpness on your budget."
You are right the Canon HV20 is a real stunner and we have been using it along side 2 Canon 5D Mark II's for over 3 years, the 5D images & video from a 35mm sensor are better at a price, but, on a split screen you may not notice .
However, setting the HV20 to cinema mode will in my opinion degrade the image , softer (as Steve says) you may like that.
So set it on say Program AE or TV mode and it will select the sharpest possible aperture, say F11 to F22.That is what you have done, I think. You will need a 1920x 1080 monitor for best results to compare.
My grand daughter has bought a Canon 600D ( it is equipped with an EF-S Lens for the smaller sensor not the EF L Series Lens for the pro cameras., I have not used it, but, regardless, if it is similar to the 5D Mark II
#go into,
You can improve the sharpness by adjustment in the camera Menu.
#1. MENU>
PICTURE STYLE> scroll down to say > Landscape>Click on >INFO Detail Set and you will have a menu of, Sharpness, Contrast, Saturation, Color Tone.In
Sharpness you have 7 levels to tune your camera to, try it. You will need to use the dial on the rear ? Read the Manual, you should not have that issue.
The problem you have is that the Lens designed for that camera may not be as professional as the EF L series professional lens System designed for the 35mm Sensors of the other Canon EOS Cameras.
We have been in the image business for over 30 years and the images out of the 5D Mark II is as good as or better than that out of a Zeiss equipped Hasselblad, a medium format camera.
You will get it right or go back to Canon Service and get them to check it out.
Incidentally , you can buy the EF lens for that camera at a price, but,the zoom length will change as will the wide angle coverage.
Freelance Imaging & Video
AUSTRALIA