This is a really nice site on Soviet visors covering 1943-1991.
As you can see, there also was a wide variety of Soviet organisations that were uniformed.

Like the East German visors, the later ones are low-quality (plastic visors and vinyl sweatbands), but the earlier ones are better quality.
The General/Marshall parade visors are of the highest quality (even up to 1991), and feature direct-embroidered bullion with patent leather visors.
(& I agree, from an aesthetic perspective, they can’t touch the TR visors).

Check it out here:

Under the Red Star; understanding the uniform visor caps of the Soviet Army, Navy, Air Force, security forces and civilian agencies of the Cold War