Neither is democracy any more stable. Most democracies before the US (and some after) did not last long due to the difficulties of starting one. After the US got itself established, democracies had more of a fighting chance because the US generally supports them. Communism never really had a country where it went into a stable state (the revolutions which led up to establishing them did not help) so there was no role model or guiding hand to keep them from becoming totalitarian states.
However, Democracy/Capitalism have the same problems as Communism when it comes to long term success. After a while, people in democracy realize that by voting for people, they can get more money. At this point, they do not vote based on the competence or political views (unrelated to money) of the candidate, but on how much money the candidate pledges to give to them. In a similar way, people in communist states (to each according to his needs) realize that no matter how much they work, they will still receive the same amount of money. Even in socialist states (to each according to his contribution), people realize that, much like in democracies, they can influence the amount of money they receive. Either way, the government will slowly devolve into a totalitarian state.
I am not denouncing either of these ideas, though. They are the best methods by which we have come up with for governing, and may be the best we will ever think of. The United States has done very well over its 200+ year course. Nothing can really be said about communism, since at this point it is still waiting to be actually put into practice and not be used as just a slogan. Unfortunately, the US is already showing signs of decline: the national debt is growing as politicians try to bribe voters with even more money while corporations and banks gain even more power (Oligarchy, anyone?). All this will be solved when we get some angels to govern us, but until then, this is the best we've got.
It's a naive, domestic operating system without any breeding, but I think you'll be amused by its presumption.