I have googled how to downmix from 5.1 to 2 and found out these forum topics:
The key is to find out appropriate downmixing coefficients which define how much of each input channel will be included in each output channel. As far as I understand, there is no silver bullet here. It really depends on the source and it is quite subjective. A player usually have a set of default values for these coefficients, but they can be different for another player. They can even change from one version to another of the same player. And if player A gives (subjectively) better results than player B for DVD X, this doesn’t mean that it will also give (again, subjectively) better results for DVD Y.
Hopefully, downmixing coefficients can be included in ac3 and dts files and some DVDs come with audio tracks containing these coefficients – most probably chosen by the sound engineer or alike. I don’t know if audio tracks in my DVD in question has them. I don’t know how to check this (yet), I will look for it when I’ll have the time. Until then, since I am looking to reproduce the DVD audio as close to the source as possible, I will stick with the 2ch track which is (in theory) downmixed/mastered by the sound engineer. Of course, there is the sad fact that 2ch track has lower bitrate than 6ch tracks (if they are comparable at all), but I still think, at least for now, that it is better than subjectively mixing 6ch down to 2ch.