So it seems to be pretty much same procedure for both EU and non-EU citizens (except EU citizens are obviously not asked why are they entering Schengen area, since they are allowed to move/work there if they wish to).
Reason why I asked is that I saw pretty long queue at "all passports" in BUD couple of days ago, but that's probably because flights from Pristina and Istanbul landed few minutes ago and they treat these citizens differently. Thanks for all answers