The lateral resistance of a lee board begins at the water
line as opposed to centreboards which begin at the bottom of the hull. For this reason they provide shallower draft while presenting the same area of lateral resistance. Disadvantage is that they have to be lowered / raised when changing tacks. Aesthetics are a factor, one way or another depending on how your tastes lean.
As mentioned previously, lee boards have the advantage of providing uninterrupted interior space, great for a tender. Overall, it's a simpler design with less chance of jamming than a centreboard. It would also be easier to convert a non-sailing boat to a sailing one using lee boards.