Apart from writing less code, are there any other benefits for using the Ternary operator as opposed to the full if/else statement?
Better readability, in some cases... I think that's all.
Is there a performance increase, less compiled code, or anyhing else that would benefit me when using it?
No, nothing significant. I think it will usually compile to the same IL anyway...
So eventually, you should only base your choice on readability. When it's more readable to write a full if/else, do it. If it's a very simple ternary expression that is easy to read, go for it.