Is it possible to get benefits of the two approaches (majoritarian and proportional) in a parliamentary system by making the lower house get elected by First-Past-The-Post and the upper one by party-list proportional? Like say: 600 representatives by FPTP and 90 senators by at-large PR? Could that mixture be the best compromise for all?
Not only is it possible for nation states to use multiple voting systems in different legislative systems, but some are already doing it. As an example from the "A"s, Australia uses the Single Tranferable Vote (a proportional system, though not a single constituency list one) for its Senate, and instant-runoff (a single winner preferential system) for the lower House of Representatives.
Whether this system (or any other) is "best" is far more complicated, opinion-based and dependent on your prior prejudices. A usual argument in favour is combining the advantages of having a single geographical representative in the larger house with a breadth of views in the smaller. Counter-arguments include the greater difficulties and need for voter education with multiple systems and the complicated question of why one house is, or should be smaller than the other (this is much easier to defend in a federal system where one house is representing the interests of the provincial governments, rather than the people, than in unitary systems).