I vote panniers of the type that hang from a standard rear bike rack, hands down. They keep the center of gravity low, generally have some side pockets for keeping bike gear separate from the main compartments, and usually have some compression straps to cinch up the panniers and keep them from flopping around with a small load or keep things like produce from bouncing around. I can get a decent amount of groceries into them, but even in good summer weather still have to do a grocery run with the car for bulky items or a big restock.