So, the same as any big urban center anywhere has better infrastructure and cultural life compared to villages and rural areas? Or was it particularly pronounced in the USSR?

Not just the USSR, Warsaw Pact countries in general (e.g. Prague was disproportionally well funded in Czechoslovakia in comparison to other cities - even accounting for its size and population) and probably authoritarian countries in general tend towards it. Of course in general the biggest cities/capital cities tend to be richer than smaller/less important cities but the comment was about the magnitude of the phenomenon in the USSR.

In the USA, we tend to hear a lot about "urban/rural divides". There's always a lot of calls to narrow or erase that divide. The efforts are usually directed towards increasing rural access (to anything, broadband, healthcare, schooling, etc), rather than making improvements for both urban and rural problems.