Is there a difference between using AES-GCM 256-bit encryption, or using SSL/TLS to pass data over a socket.
I am currently passing data back and forth from client to server, using asymmetric AES-GCM 256-bit encryption. Is there an advantage to using SSL/TLS as opposed to my current security method?
difference between using AES-GCM 256-bit encryption, or using SSL/TLS

These cannot be directly compared.

AES-GCM is encryption with integrity protection - nothing more.  It needs an encryption key which somehow needs to be exchanged between the sender and recipient - how this is done is out of scope of AES-CGM.
SSL/TLS is a protocol specifically to protect a communication between two parties.It provides encryption and integrity protection (for example using AES-CGM), but much more:  Key exchange to compute a common key which is then used in the encryption, replay protection, authentication of the server to protect against man in the middle attacks.

Thus, better use SSL/TLS since it provides not only encryption but much more of what is needed for secure communication.
AES-GCM 256-bit VS. SSL/TLS for socket security