Purchasing new iPhone — from verizon.com or apple.com?

One of our phones is eligible for upgrade, and the contract has ended. If I purchase a new iPhone online from apple or a new iPhone from verizon is there a difference? The price is the same, but I have had verizon tack on some unwanted services, fees or contracts many times before. I just don't trust shopping on the VZ website.

TLDR; Are they the same or is one better?

EDIT: I'm on the Verizon plan