Convert 1920x1080 to PAL - DVD This question differs from how to burn full hd movies (1080px720p) in DVD because I would like to know how to convert the video in this resolution to DVD without giving up too much quality.

I used Any video converter to convert my 1920x1080 video to a PAL-DVD. Since the max resolution of a PAL-DVD is 720x576 the video looks very pixelated. Also the original video with a 16:9 format filled my full screen. The dvd has now black bars on the edge, since 720x576 is not 16:9 ratio. 

I know that great movies like lord of the rings are out on DVD, in 16:9 format and look great. How did they make this possible with a 720x576  resolution?
I have not tried Any Video Converter, but I did try HandBrake, and it works reasonably well. DVD-Video allows up to 9.5 Mbit/s bitrate, so do not be stingy, allow at least 5 Mbit/s or so, considering that free encoders are not very efficient. Make sure frame rates match, or convert without judder or ghosting. Make sure you convert between progressive and interlaced correctly. Make sure your luma is encoded within DVD legal range, otherwise your image will have too much contrast and will lose near-black and near-white detail. 

704x576 can be 4:3 or 16:9, plus 8 pixels on each side for digital blanking. The best looking DVDs I authored were 24p ones because they have full vertical resolution. I am not sure whether 25p DVDs can be authored as true progressive DVDs though. Interlaced DVDs look rather sad on a big screen.