I hesitate to write this because unfortunately I've forgotten the source of it. It might have been Azriel Lorber's "Misguided Weapons", or Brian Perret's "Last Stand", or possibly some other similar book. Anyway, here it goes:
Reportedly research by US Army after WW2 found out that only some 20% of all allied soldiers actually shot at the enemy intending to kill him. The other soldiers just shot in the general direction of the enemy lines, because they could not make themselves to actually kill a human being. Now if the enemy had 40% of such - let's call them warriors - in his units, he was twice more effective in combat. The book I read claimed that this percentage of warriors was much higher in German units than anywhere else. 2 main factors were named - training and attitude. Reportedly German soldiers trained shooting at human sized and shaped targets (silhouettes), while for example British soldiers used circular targets (concentric rings). As to the attitude, the German soldiers saw their service also in terms of sacrifice to Fatherland and thus were more ready to risk their lives. The book also named a third factor promoting this wilingness to kill - hatred, especially caused by an atrocity made by the enemy. That was mostly visible in the Asiatic theater, where Allied soldiers generally didn't have any problems shooting Japanese soldiers, especially after they saw an atrocity like destroyed hospital or something similar.
Now if we follow this train of thought it is plausible that elite units should have better and more realistic training promoting higher combat efficiency. Further, in case of armed forces in exile - it is also plausible that in such case this ability to kill could be higher than in other armed forces if the soldiers had to overcome obstacles to join said armed forces in exile. Then only the real warriors, able and willing to fight, would bother with illegal crossing of borders, avoiding capture and suffering all the associated hardships to join the army and fight.
Note that modern armies actually changed their training after WW2 to be more realistic. Soldiers now train at least with silhouette targets, and more and more using virtual reality. In some militaries soldiers are even desensitized to violence during their basic training. It would further support that the book I read was actually onto something.