Yes. The portability of identity and data is the key differentiator I believe. But could a relay owner require that you only use a client they approve in order to access their relay, thus trying to lock users in and prevent them from leaving?
Discussion
yes, they can require anything they want. users can leave but they might be left without features those services provided out-of-protocol. there's no way you prevent someone to use their identity somewhere else. you can loose content if those services used private relays for it and you don't have a copy yourself, if you have copies and they adhere to NIP01, then you can repost them to other relays.