Its easy to see what Luigi is going to do and weave around his hit-boxes. He has virtually no maneuverability while airborne, even though he hangs in the air for so long. This tends to work against him.
So when he comes down with a nair you can simply wait and usmash and outprioritize his nair or just jump around him and bair.
What's worse, if you predict things like ledge-hops or down+bs...you can SUPER punish him. You block a tornado and it leads to an usmash which will kill in excesses of 80% on most levels. You block a ledge-hopped fair/dair/nair and jump out of shield and shine him for a kill as well. Without a double jump he's screwed.
These things are all dependant on IF you can force him into that type of situation of course. Still, having so many efficient ways of destroying him as a character makes it almost impossible to win. Then again, you have the rare gems like Ka_Master - who wreck Foxes left and right.
Bottom line is: if the Fox doesn't get grabbed and/or plays out of his shield like he's supposed to, there should be no way for Luigi to even start a combo, let alone catch him or grab him.