Break Dancer: You would do both. On most modern aircraft with a switched on crew and a little organisation the seeds of where the nearest suitable airfield is would already be well sown. With no aircraft non normal situation planning a diversion is pretty simple and opening up the fuel jettison is something that can be done while transitting to chosen airfield.
I can only speak for the 777 but it is very simple system that dumps to max land weight automatically, even calculating the fuel burn to the div once the FMC has been programmed which takes about 30 secs.