What is the difference between using Private Properties instead of Private Fields
private String MyValue { get; set; }
// instead of
private String _myValu
When dealing with private access, the differences are very small. Yes, there is a performance hit (which may be optimized by the JIT) send properties represent a method call, instead of a direct address access.
The main advantage to using properties is to allow changing the implementation without changing the external signature required. Since these are privately accessed, any changes to the implementation only effects local code.
When dealing with private members, I see no advantage gained from properties, except for your team's conventions.