I do think comparing fascism and communism as forms of political ideology is easier, certainly and no, I don't think the economics are relevant in the sense you address (though comparisons are valid on any other number of areas). Not entirely sure I accept communism as only being an economic system - by definition it has to have political control over the entire economy, with consequent implications for areas ( e.g. the state acquires the need to increase productivity and loses any incentive to protect worker's rights).
 

I did wonder if this was where you were going, which was why I cited Jared Diamond. Here's a sample (please note that this is a contested subject )