While every day/species is different and it changes without any notice, in general lures are much more "species specific", where as "natural" bait tends to catch more, but not necessarily what you were looking for.
ie: Trolling for billfish a lure generally will get you a billfish, and the size often determines the probability of the size. But you will get more action, not only from billfish, but pert-near everything else, if you use a nicely rigged ballyhoo.
The same general idea holds true even if sitting and bobbing under a rig...
Note that ( as you already likely know ) "conditions" pretty much pre-select the sub-set that might hit the line. ie: "green water" likely a sailfish ( in La waters ) and cobalt blue is more likely a Blue Marlin. On a rip, look for the mid-range predators, dolphinfish, wahoo. And so on etc blah, blah, blah...