Your grandfather probably did not encounter any Waffen SS formations in Italy, as they were employed largely in NWE and on the Eastern Front. Contrary to their popular image, SS formations were mistrusted by senior Germany army officers as they tended to be lacking in tactical skills and all arms coordination, as opposed to strict adherence to ideology. The latter led to too many frontals and gut feel reaction immediate counter-attacks, and lack of attention to the rules such as the Geneva Convention.
The German paratroops, on the other hand, were generally respected - Lockie Fulton, who commanded the Royal Winnipeg Rifles from the Leopold Canal to VE Day, told me they were the best soldiers he had ever met - , and even the average German formation was rarely a pushover. The German army also tended to observe the rules. I read in the last couple of days an account by a member of 6 Airborne Division who was badly wounded and lying in the open. A German medic ran out and tended to his wounds. When shells began to fall, the German protectd the British soldier with his own body and then stayed with him until other British soldiers arrived. The wounded man acknowledged that he owed his life to an unnamed German medic.