I would recommend PNG over the GBR any day of the week...
The hard coral formations in Milne & Kimbe Bays knock the spots of anything on the GBR!
And the big fish action, as Don says, is better in PNG, particularly in the northern areas such as Kavieng and the Hermit & Ninigo Islands and the Eastern Fields out of Moresby.
Best time of travel for PNG is April - June and September - November.
For the GBR, well Jan - march is traditionally cylcone season, but if there are no cyclones arround the conditions can be perefect. Avoid July & August like the plague and you would be fine. October & November would be the 2 best months for assured weather for a trip to the Coral Sea.
Hope that assists.
Regards
Jim