"Are you a lawyer?"
In the first approximation, nothing. In the second approximation, which is perhaps not part of any language course of around A1-B1 levels, I would say 'Ügyvéd vagy-e?' adds a certain flavour to this question which keeps the conversation at a colloquial / friendly / more informal / lower level. 'Ügyvéd vagy?' is colloquial alright, but, to me it is dry, formal, cold, empty. I would imagine that the addressee of this inquiry would almost reach for his/her certificate to prove that he/she is indeed a lawyer. As a matter of course, it is difficult to build any context from short questions like these. Just my $0.02.
'Maga' is a personal pronoun for 3rd person singular (the plural form is 'maguk'). It is formal, but not as formal, as 'Ön/Önök'. There happens to be yet another, old personal pronoun: 'kend', of which plural is 'kendtek'. These are not very formal, but rather somewhat pejorative. E.g. 'Ügyvéd kend?' (I suggest that you do not try it in the lawyer's office.)
'Vagy ügyvéd?' is not correct. 'Ügyvéd vagy?' is.
'Maga/Ön ügyvéd?' and 'Ügyvéd maga/Ön?' are all correct.
It's because they aren't alike. "Turista vagyok és rendőr vagy" misses the basis of the contrast: I am a tourist and you are a police officer. For contrasting, you shouldn't omit the phrase that's meant to make the difference in the two clauses.
Also, I'm not sure what makes you think "Ön egy ügyvéd" was superior. We may argue about levels of formality but that "egy", to this day, would sound awkward for most of us.
There is an even bigger problem than the rejected translations discussed already. One of the completely correct translations of this question is "Te jogász vagy?" (Problem 1: "You" also means the informal "te". Problem 2: "lawyer" means "jogász," not "ügyvéd." Nevertheless, this version is not accepted as of January 13, 2021. This is completely wrong from Duolingo. The word "lawyer" primarily means "jogász" and not "ügyvéd." The meaning of the latter word in Hungarian is closer to "attorney" (U.S.) or barrister (U.K.). This mismatch is a problem throughout the Hungarian Duolingo.
All I can say in response to that is that the word ügyvéd appears routinely outside lawyers' offices and is fully understood to mean anyone who practices law. I have never seen or heard the word jogász although jog and törvény certainly are used as translations for law. You're absolutely correct in saying that jogasz means lawyer but the word has nothing like the currency of ügyvéd in Hungary. Also, unlike the UK, there isn't the same division between solicitors and barristers with differing rights of audience depending on the level of the court or whether higher rights of audience have been obtained as is the case for some solicitors.