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?