I'm going to be frank here, this isn't going to be a detailed discussion on two complex topics that, quite frankly, 99% of the people who have a strong opinion on either one have almost no knowledge of the subject. Protip: If someone believes there is or ever has been an actual communist country, you can instantly and always disregard their opinion on the topic, lest they defend their answer by clarifying a countries attempts to create a communist ideal by forced industrialization of the country. No country has become communist as Marx saw it, or even as it changed through Lenin and Stalin.
However, that's a bit of a tangent. My real point is simple, unsophisticated yet, at it's core, pretty accurate.
Communism is the silly notion that, if we escape our capitalist system, everyone will stop being greedy, hateful, bigoted, and selfish. We will realize we're all fellow humans fighting the same struggle. We won't need a government, because everyone will help each other. No one will take advantage of anyone else, once we escape the capitalist system and realize it has tainted us. Despite the idiot Republicans ignorance, Communism's end goal is the abolition of government... you'd think these small-government idiots would read a book and learn a bit about what they hate but hey... educational books and Republicans rarely mix.
As simple as I make it sound, at it's core it is a silly notion, with many complex layers on it. And one that ignores every bit of evolutionary and psychological evidence we have (though I won't hold it against something from 100 years ago) It would never work, as Marx would have wanted.
Now, Free Market/Economic Libertarianism is the goatee'd version of communism, sadly enough. Rather than the idea that we should all help each other and that we're all equals fighting for the same cause and as such we should all have each others backs, so to speak the Free Market ideal is, well, evil. It is the idea that if everyone is completely selfish, greedy, spiteful, and self-serving then everything will work out. If everyone takes advantage of each other as much as you can, then only the most evil/born into wealth human beings (or business savvy, if you will, often the same thing) will rise to the top and everything will sort itself out and we'll have a utopia. The sad part is, this is more accurate and less simplified than my communism portion was, yet just as if not more accurate at the core.
Now, to be frank, I can write books on why free market libertarianism is foolish in nearly every regard. I can do a book or two with communism, albeit for far different reasons. The main point is this:
I have more knowledge on these subjects than the vast, vast, vast, majority of people. (This is not a fact that makes me look good, since I'm no PhD holder on the topics, it's rather a depressing statement about everyone else) Yet the painfully ignorant super-majority will defend whichever side they happen to have an emotional attachment to (as noted, their ignorance makes it impossible to have an intellectual attachment)
So here's the short and simple point. There are two people who are ignorant of the intellectual merits of the subject, but have emotional connections to them -- so lets break it down emotionally.
Communism emotion: We need to help each other out, stop being greedy and worried about what we have. Rich or poor, we need to help each other out, and then we'll find that to divide people based on wealth is the worst form of discrimination. Realize we're all in the same boat and we all need to help each other paddle. Break away from greed and lets have a world were everyone is being taken care of.
Free Market emotion: Be a greedy asshole, fuck everyone else. If you were born into a rich family and went to a good school with no worried as a child, then that means you worked harder than a poor kid who had a million roadblocks towards his success, including a vastly inferior education for his entire life due to circumstances out of his control. Everyone just needs to be completely selfish and then, eventually, the selfishness will balance everything out.
Pick someone who leans more towards communism realistically, low to moderate socialism, since it's basically impossible to be a classic communist now. It's sort of like supporting the idea that all illness is caused by the four humors. It makes no sense, you're trying to support an idea that has been dead forever and is impossible to even work into a modern framework.
Pick someone who leans towards free market libertarianism, which is just as silly as old communism, but still alive sadly. Compare the emotional simplifications of the two people. Conformation bias aside, it's fairly accurate, particularly since the beliefs are held due to emotional appeal rather than intellectual for the vast majority of both sides. The person leaning towards socialism will on average be more understanding, caring, and compassionate. The free market person will believe that every handout he got, every advantage they got, was their own doing. They often think helping others should be completely removed from the picture and everyone should be as greedy and wealth oriented as they can be.
Quite frankly, you can pick up strong emotional cues from core beliefs in the vast majority of people, and it's scary at how they correlate.