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The conventional wisdom is that jib-headed rigs offer better upwind performance, whereas gaff-rigs are often felt to have an advantage deep downwind. There is extra complexity to the gaff rigs, including at least one extra spar, and some different sail handling techniques (you must remember to scandalize the mainsail when jibing in very heavy air, for instance).
Jib-headed rigs have won-out (in the mainstream anyway) because of their relative simplicity. But gaff-rigs still have plenty of adherants. In addition to the off-the-wind advantage, folks like them for their traditional looks, and they are also favored (primarily by trailer sailors) because the mast is smaller and more manageable for stepping. There are some production boats still using gaff-rigs, like the Catboat builders up in New England (but even they offer jib-headed rigs as an option on some models).
Do you have a specific boat you are looking at that has a gaff rig? Or are you just asking theoretically?