About visiting the Great Wall of Beijing, I would visit the Simitai if I were you. I had seen photos a friend took there and it worth all the effort getting there.

I know nothing about Mutianyu. I recommend you not to visit the Great Wall through Badaling. It is a very hot spot in Beijing that it is too crowded with tourists all the time. You may not be able to sense the spectacular of the Great Wall here. I had been to Badaling more than ten years ago (and it was already very crowded. I will visit the Great Wall again in the coming years most probably at Simitai.

Best regards, Sera Hong Kong