I'm pretty sure this is supposed to be the opposite (jealousy means you want something the other has, envy means on top of that you don't want them to have it anymore) which is why envy is the cardinal sin, not jealousy. At least I remember very distinctly being taught it that way in school.
Jealousy comes from feeling like something is taken away from you, or you have less than someone else.
Envy comes from wanting others to be miserable regardless of whether it will make you happier or not.
I have never heard of them being the other way around. Actually, just checking the definitions right now, I see for jealousy "fear that something or someone might be taken away from you" and for envy "to bear a grudge toward someone due to coveting what that person has or enjoys"
It seems to me envy is the "worse" and pettier one, personally. Jealousy is an inward feeling that makes you feel miserable for what you don't have, envy is an outward feeling that makes you hate someone for what they have.
EDIT: from a website that compares the two:
A person envies someone towards whom he has ill will because of that person's success, achievements, and the like. He envies something that belongs to someone else and to which he has no right or claim. He is jealous of intrusion onto something that belongs to him or upon which he maintains a claim.
An envious attitude is always negative. A jealous outlook is usually negative but it can be positive, depending on its object and inclination. For example, a man may be jealous when another man talks to his wife (negative); however, a free people must jealously guard their liberties if they want to keep them (positive).