The Teutonic Knights were an offshoot of the Knights Hospitaller specifically created to aid and assist at a German hospital in Jerusalem.
The Knights Hospitaller were a group created and primarily charged with aiding and assisting travelers to the Holy Land - the poor, the sick and the injured.
The Knights Templar from their inception were a group of warrior monks who protected pilgrims as they traveled the Holy Land.
Of these three groups, only the Knights Templar were - from the very beginning - fighters. The other two groups did, eventually, change their charters and become fighting groups and all chose different paths for their Orders.
As to which was the best ... I'd be hard pressed to decide that. If I were a pilgrim being attacked by infidels, I'd say the Templars were the best. If I were injured, I'd say the Hospitallers were the best. If I were German and injured, I'd say the Teutonic Knights were the best.
I'm a Freemason.