The problem is that we were never shown Zaheer's past and what he was capable of. We are only told about them. Without seeing Zaheer's prior abilities it's hard to see the differences. Because most of our knowledge of Zaheer's past is hear-say and it creates more speculation that actual fact.
Yes, I agree that Zaheer would eventually use all airbending, but not at the start. I expected him to gradually improve and use more airbending. But he mostly used airbending even from the start.
As someone who pratices Martial arts including Bagwa (airbending), I can tell you that it takes time to learn different forms. Excellence in one form does not guarantee excellence in another.
Zaheer may studied the air nomads, but that is no substitute for learning form a teacher. There are so many things about martial arts that you can't really learn from a book.
I agree with lego, the were pretty evenly matched even though Tenzin was a true master.