I've seen this argued to death from both sides.
Puerto Ricans do not pay Federal Income tax, but they do pay into Social Security and Medicare, and are eligible for some benefits.
Puerto Ricans cannot vote for President.
Puerto Rico has it's own Constitution
Puerto Ricans claim Puerto Rican and US citizenship. Some also claim Spanish and European Union Citizenship.
The US Gov't and Puerto Rican Gov't both recognize Puerto Rican as a separate nationality (i.e. not American).
I tend to think that while Puerto Ricans have some American rights and benefits they are not full citizens. They would not be full citizens unless Puerto Rico became the 51st state.