I prefer the first one.
When I see a little overexposed photos from others, they often like me. But when processing I prefer to make the photo more contrast. It seems to me that in this photo you have slightly darkened and gave drama to the sky. I think that I would definitely try this option myself.
I gave contrast to the foreground and model and brightened the sky. 2nd picture is my edit :P
It's funny that I did not guess. But still I would go along the path of darkening the sky. Although I understand that this may not be the best method. Especially when processing a portrait. 8)
there's no right or wrong way. All's subjective.
I don't like unnatural/heavyhanded processing. The gradient was too harsh and too dark for my taste and the model didn't have enough contrast to shine out from the image. I gave it a more sunny summery spin as opposed to the original cloudy bleak style.