Any quality and coverage difference between contract and prepaid?

Hey all, I'm thinking about having Verizon as my career when I get into the United States as a student. Since I don't have SSN, I either have to put my deposit and have contract or get prepaid for my smartphone.

Is putting deposit and having contract with Verizon worth a contract? or should i just go with prepaid.

If data quality is the matter here, I would definitely go with contract putting deposit, though not sure about it since I have no idea.