Both sentences are grammatically correct, but they may sound a bit awkward or unusual in certain contexts. It depends on the context in which you're using them.
"I'll be back to the me that you liked."
This sentence is grammatically correct, but it might be more commonly expressed as "I'll go back to being the person you liked" or "I'll return to the person you used to like."
"I'll be back to the James that you liked."
This sentence is also grammatically correct, but it sounds somewhat formal or unusual. It might be more natural to say, "I'll go back to being the James you liked" or "I'll become the James you used to like again."
The choice of words depends on the specific context and the tone you want to convey.