Although the German Paratroop units never made a significant drop after Crete, they were indeed more than just "Wehrmacht grunts in different uniforms"
From a website on Normandy; Among other elite German outfits in Normandy, there were paratroopers. They were a different proposition altogether from the Polish or Russian troops. The 3rd Fallschirmjäger Division came into the battle in Normandy on June 10, arriving by truck after night drives from Brittany. It was a full-strength division, 15,976 men in its ranks, mostly young German volunteers. It was new to combat but it had been organized and trained by a veteran paratroop battalion from the Italian campaign. Training had been rigorous and emphasized initiative and improvisation. The equipment was outstanding.
Indeed, the Fallschirmjäger were perhaps the best-armed infantrymen in the world in 1944. The 3rd FJ had 930 light machine guns, eleven times as many as its chief opponent, the U.S. 29th Division. Rifle companies in the FJ had twenty MG 42s and 43 submachine guns; rifle companies in the 29th had two machine guns and nine BARs. At the squad level, the GIs had a single BAR; the German parachute squad had two MG 42s and three submachine guns. The Germans had three times as many mortars as the Americans, and heavier ones. So in any encounter between equal numbers of Americans and Fallschirmjäger, the Germans had from six to twenty times as much firepower.
http://www.worldwar2history.info/Normandy/German-soldiers.html