I would choose to turn over the 'A' card, only.
Let's walk through the reasoning:
If I turn over the 'A' and there is an even number then the statement is NOT false.
If I turn over the 'A' and there is an odd number then the statement is false.
If I turn over the 'A' and there is another letter then the statement is false.

However, the same rule(s) apply to the '4' card (with respect to a vowel on the other side).

I believe (as I think has been implied in earlier posts) the puzzle is not succinctly described and there cannot be a definitive answer.

------

"I am certain there is too much certainty in the world" -Michael Crichton