From my readings the SS units were more likely to press home an attack but they were routed off on many occassions and not just on Elsenborn ridge but right throughout the Ardennes. This is where I think many earlier wargames have created a mistaken view of the SS. Sure they had some seasoned tough nutters but by this time of the war their ranks were largely populated through conscripts not fanatical volunteers. So the level of fanaticism just wasn't what it used to be compared with the early East front campaigns. nor compared with Normandy in the West. You have to remember that the SS lost heavily in Normandy. Most of its divisions were rebuilt just prior to the Ardenne battles. In many cases the SS did not perfom as well as standard Whermacht formations.
Same with many german paratrooper units (with exception of the ones in italy maybe) serving the last half year of the war. These are oftenly considered "elite" infantry, but generally lack most of everything. German high command rated these at "IV" combat value, which means "limited capabilty for defensive actions". Like with their SS comrades, there was an above average focus on indoctrination and morale boosting measures, which made them perform more aggressive and tenacious, despite lack of proper training, combat experience and weapon/ammo supplies.
I´ve yet to find a good balance for my paratroopers in OP Veritable (2nd, 6th, 7th, 8th division and various corps/army para units). Training and experience will stay rather low, while aggression, determination and morale, as well as unit leader stats obviously would be the deciding factors.