Is exterior paint more protective than stain for protecting a shed from rain/elements?
All wood coatings are essentially decorations. The only thing that keeps wood from rotting outside is proper drainage of it and airflow around it. Wood can get wet every time it rains and snows as long as it is permitted to shed water effectively and dry out quickly. When it stays wet even through days of sunshine and wind is when wood will begin to foster fungus and rot. The vegetable and fungal organisms that attack wood require constant moisture for survival. So design your wood elements exposed to the weather judiciously, and choose a finish for its aesthetic merits and maintenance requirements. 

An oil based stain requires minimal prep work, doesn't peel and flake as it ages but simply fades, and reapplication down the road requires little to no prep work again, though it may require more frequent reapplication than paint to remain looking brilliant. Paint is a more exciting and transformative finish, but requires more prep work, and reapplication down the road may require some labor intensive scraping and sanding. If you do decide to use paint, then stick with a high quality exterior latex, and be sure to use a high quality latex primer first (you get exactly what you pay for with paint). Stay away from oil paints. Latex paints are much more flexible than oil paints and will hold longer looking good.