Question

This is not really an answer so much as a series of comments. I think the problem is that mathematicians generally view proofs as explanations, so part your question isn't quite meaningful. Of course, not all proofs are the same. Some proofs may be preferred to others based on aesthetic criteria such as brevity, clarity, elegance... To address your other point, in "if and only if" proofs, there often is an easy direction and a hard direction, but not always. Sometimes both directions are at the same level (to take a trivial example x+y = z iff x = z-y). Or it may be embedded in a cycle of implications such as A => B => C=>A, where only some links in the chain are trivial. I'm not sure if this clarifies anything, but if it doesn't, then perhaps you can reformulate the question.