My understanding is that "vrei" is "do you want" and "doriţi" is more "would you like". I am happy to be corrected.
MarkFuller7 that is also my understanding from multiple learning resources.
this question is totally nonsense. How could someone prefer a juice?
This should be: Do you want A juice or A beer... even the translation on this page says so.
I heard:"Doriți un suc sau bere?" which is logical, because one never drinks just one beer... ;-)