It's a big topic and there's a lot to discuss, but there are a few points I have thought of.

Just so we're sure of the definitions, by capitalism I mean private ownership of the means of production, market exchange and a lack of social safety nets. By socialism, I mean worker ownership of the means of production, and an economic system designed to ensure that all of a citizen's basic needs are met (in theory).

Where would a man have a better chance at getting a relationship?

Under capitalism, sex and love can be commodified, so if you lack sexual attractiveness, you can still have sex by paying for it. Under socialism this wouldn't happen unless sex work was seen as regular work and they had their own union. The government would also need to see sex work as a necessity.

Under socialism, the ability for men to offset their sexual attractiveness with other traits is kinda limited, because they can't buy love. However, one can argue that without a socially stratified society, many men who were lower class under the capitalist system are in a large middle class, making it more socially acceptable to date them.

I'm just throwing thoughts. What do you think?