The 80 and 81 grills have the mounting screws in slightly different places. Most of the header panels, you will see the little oval plastic bushing where the screw goes in (after removing the grill). Close to that location on most of the 80/81 header panels I have seen, there will be a little depression where the bushing would go in for the other year of grill. You will either have to open up those holes and move the plastic bushing or make new holes and put another plastic bushing in those holes to hold the screws. Screwing directly into the fiberglass is not really a good plan because eventually the screws will work their way loose and the grill will fall out. And as several other people have said the headlight bezels are different between 80 and 81. They will physically bolt in place of each other but they look goofy because they don't line up properly with the wrong year of grill.
The pictures that 80Malibu posted show the black accent line that goes around the bezels and across the top and the bottom of the grill on an 81. On an 80 that black accent line only goes around the perimeter of the bezel, not across the grill.