So, their constitution says the same thing as our constitution? Shit....
"Shit"? lol, okay I'll dumb it down for you.
China has but one political party, the Communist Party, codified in their constitution. Our Constitution mentions not rights, obligations or prohibitions on politcal parties. So to infer we are a democratic republic with a constitution is the answer.
The OP asks to choose between Capitalism and Democracy; the proper question to ask is between Capitalism and another economic theory, or between democracy and a monarchy, a plutocracy, an oligarchy or many other types of government in theory and in practice.
See:
Political Parties | Udfl