Before I attempt answer the question of Capitalism Vs. Communism, let me first say that I do not propose to be an authority on either subject. I'll agree with your stipulation that both have noble goals, but unfortunately their methods are not equally successful. Actually I think that if communism were able to exist in a pure state without human corruption, it would easily beat capitalism, for pure capitalism would be cruel an unmerciful. This is why I think that capitalism must have some limits (which it has in the US) to be successful.

As far as the problems inherent in Communism, Communism relies on the state being uncorrupt, as well as the individual producing the goods. The state must be able to evaluate the needs of the common man and distribute goods accordingly. The individual must be willing to produce all that he or she can for the good of others, an act that unfortunately contradicts human nature of selfishness. Instead you'll have people competing for the servicing of their needs, not their production. Production ends up lower because people are unmotivated (“it doesn't benefit me") , and society as a whole suffers. Note that if people could overcome this selfishness, then I think communism might actually work. I have observed with some humor when watching Star Trek: TNG recently that this is exactly the system that Rodenberry foresees in the future (no money, everyone works for the common good).

The brilliance of Capitalism, however, is that it utilizes human selfishness to benefit society. People must compete to produce the most, because that will cause them to gain the most. The evil inherent in this is that in a pure statue you have economic Darwinism, where the less-able-to-produce are treated as if they have no value and are cast aside. A very real ill effect of this in the US is that educators are paid WAY below the amount they benefit society because they are not valued like they should be.

Still, I believe that Capitalism will always end up the victor until humans overcome their natural selfishness.

Edit: Also, this is only the economics. The Atheism of Communism is a deal killer for me.