This is one of those debates that can go on and on forever. :twisted:
In any case one can find features that will point towards one or the other species.
If you look at
blue marlin pictures (or have seen a few in action) you will notice that their dorsal never folds down to the point of disappearing and that their pectoral fins are anywhere from black to neon blue (never white). And if you look closer at the first picture of the fish coming upside out of the water you will see right above where the fish is touching the water there's a part of a fin (or sail) sticking out that a blue wouldn't normally have.