On your question: I haven't lived in USSR (born in Russia already), but from what I could gather from relatives and older acquaintances, it was quite similar.

Generally good on workplace equality, quite some everyday/domestic sexism going both ways. One negative change in the workplace since the fall of USSR and rise in private enterprises is reluctancy of some bosses to select female employees, as they are feared to take maternity leave and be on the company's budget. I wouldn't say this happens everywhere, but it's common enough to be notable.

The positive shift in the domestic part started about 2010's, as new wave of feminism has been accepted by many in the Russian youth. Still, there are some issues on that front, particularly outside big cities.

In any case, the Soviet legacy clearly shows, and it sure has helped immensely, especially in the workplace.