Both see a system of an unregulated “market” that is highly responsive and productive.
Both tend to think a ‘central planner’ will predict what the ‘market’ will want far better than millions of independent actors acting upon their own best interest.
There is a good reason why the Soviet Communists rejected Darwin's theory - it smacked too much of Capitalism - with independent actors acting in their own self interest - a ‘reward’ for ‘individual excellence’ - and no easy way out of the reality of “no such thing as a free lunch”.
The Darwin family was not "used" by the eugenics movement for their name, they FOUNDED the eugenics movement.
As for your assertion that the communists rejected Darwinism, that is completely unfounded. The ONLY people who try to say this are Darwinists.