Now I haven't read through the 1936 Constitution, just read a few lines in there. I could see it's fairly the same, at some places it was copypasted, some lines were redrafted (I've no idea why, wouldn't make a difference), I did not read enough to find anything meaningfully different.
Judging by the general tone we could mistake these two with a constitution of a more or less actual democracy of our relatively free world.

But here's a fun detail.
There's some socialist gibberish in ours, here's one I translated:
The Hungarian People's Republic relies on the conscious labourers' organization to administer its functions. In order to defend the order of the people's democracy, to take an increased part in the socialist development, to widen the cultural education, to realize the people's rights, to nurture the international solidarity, the workers can establish trade unions, democratic woman, youth, and other mass organizations, and combine these forces into the democratic People's Front. The close cooperation and democratical unity of the industrial, agricultural, and intellectual workers is materialized in these organizations. The leading force of the state and societal activity is the working class, which relies on the democratic unity of the people and led by its vanguard.
I tried to remain as literal as could, didn't allow much poetic liberty to myself.
And here's it's parallel from the Soviet, Chapter X. Article 126.:
In conformity with the interests of the working people, and in order to develop the organizational initiative and political activity of the masses of the people, citizens of the U.S.S.R. are ensured the right to unite in public organizations--trade unions, cooperative associations, youth organizations,' sport and defense organizations, cultural, technical and scientific societies; and the most active and politically most conscious citizens in the ranks of the working class and other sections of the working people unite in the Communist Party of the Soviet Union (Bolsheviks), which is the vanguard of the working people in their struggle to strengthen and develop the socialist system and is the leading core of all organizations of the working people, both public and state.
Oh yeah.