I'm looking for a comprehensive pros and cons of the two most commonly used station-keeping types of orbits used at libration points, Lissajous and halo orbits. When would one select one over the other and why? Do any of the criteria change depending on which Lagrange point (L1-L5) and libration points of which two bodies one would like to place an artificial satellite at? Or is this more mission specific, and depends more on what these satellites are doing there and how wide of an orbital box they require (say, to avoid transits through Earth's umbra or penumbra)?
Ideally, I'd like to see some mission design for which both types of station-keeping orbits were considered, and one chosen over the other based on some documented criteria. Perhaps ARTEMIS or ISEE-3 produced some detailed documentation about this? But if that isn't available, let's, for the sake of argument, pretend that I can't decide between the two for JWST. Why would I have picked a halo orbit for it, and not a Lissajous one?