How many legislature members there were who were not members of any party in the USA compared to the USSR during the Cold War and now?
For the USA, I guess the information is reasonably googlable. But as for the USSR, I wish to point out that the answer is: 0, both substantively and formally.
(1) Substantively: Clearly, no one who was really opposed to the CPSU was allowed to come within a shout of any political office.
(2) Formally: The "independent" candidates were actually running as part of a "Communist and Party-less Bloc" (which pretty much covers all bases). So even if they were not card-carrying members of the CPSU they were elected to the Supreme Soviet on behalf of the CPSU. I couldn't find an English reference to the bloc, but here is a Russian one from the Big Soviet Encyclopedia itself.
EDIT: Here is a contemporary reference to the bloc: http://ufn.ru/ru/articles/1937/8/b/.
EDIT: The second source I gave is a contemporary, 1937, official propaganda press release about the elections. Curiously, it was published in a physics journal (and presumably, in other journals as well). The following passage is telling:
Быть депутатом Верховного Совета первого в мире социалистического государства , состоять в железной когорте партийных и непартийных большевиков , коим доверено руководство могучей , непобедимой социалистической державой , — почетное и ответственное дело . Величайшую ответственность перед народом , перед своими избирателями должен всегда чувствовать каждый депутат.
In English (my translation):
To be a member of the Supreme Council of the world's first socialist state, to be part of the iron cohort of Party and non-Party Bolsheviks, to whom entrusted the leadership of a powerful and invincible socialist power - is a matter of honor and responsibility. Every deputy should always feel a great responsibility to his electors.
So, the deputies formed an "iron cohort of Party and non-Party Bolsheviks". I think it proves beyond any doubt that the "independents" were just as beholden to the party as the formally party men.
UPDATE: I found a 1947 election poster for the "bloc".
UPDATE: More evidence: a booklet, published in 1954, titled "The Indestructible Bloc of the Communists and the Party-less". Published by the State Press for Political Literature.