I read once (it's been a few years and you know how these "facts" change over time) that you don't start burning fat until you've been riding a bike for 90 minutes (and I assume this means riding in the fat burning heart rate zone).
I will grant you that burning fat and being healthy are not the same thing, but it does tell me that you would need to be on your bike for a longer amount of time to get the same workout as a 30 minute jog. For most people, myself included, an hour a day of getting away from the house is a rare luxury, so a 30 minute jog in the morning is what I choose to do for exercise. I mostly commute with my bicycle (and when I do have the chance to go on a nice long bike ride, I don't think of it as exercise in the same vein as jogging).
If time constraints were not an issue, I'm not sure what would be a better workout, but certainly neither one of them on their own leads to good health. Like the other posters have said, good nutrition and using other muscle groups is required.