I agree with the common thought of "you can always learn more/you are never done improving" - But, if I had to identify the hallmark of what I think an "advanced" brewer is -
CONSISTENCY. When you get to the point that you can nail a recipe time after time after time and turn out the same great product, when you can brew a beer and KNOW which variable you need to alter next time to get the beer you want, and then do it ...... To me, if you can do those things - you are an advanced brewer. Not to say that you can't get better, but you have reached the point where you are better than the vast majority.
This is my goal..... If/when I attain it, I will feel comfortable with the "label" of advanced.