While you point out the most likely contenders for the "top spot", as it were, the question is essentially unanswerable in an absolute sense. As far as I know, there's no way to measure the requisite values we'd need to reach a conclusion, such as average skill at arms, discipline, and courage. On top of that, those Orders could sometimes be fighting very different opponents in very different situations; the Teutonic Knights, for instance, tended to remain within Europe to wage war against domestic polytheists, whereas the Knights Templar are obviously famous for their involvement in the Crusades for the Holy Land.

While this diverges from the question somewhat, I think considering these Orders for how militarily elite they were misses part of the point. After all, when one is trained and equipped as a mounted knight, they occupy the same essential league as other trained and equipped knights. What's really unique and relevant about these Orders is the interaction of religion, civilian consideration, and military action. For instance, the Teutonic Order began as a medical order that was specifically German, to help solve the problem of there being very few German-speaking medical practitioners in the Holy Land. It was from there that the Teutonic Order grew into a domestic crusading military power. And the Knights Templar had as much to do with banking as they did with warfare or religion.

What makes these Orders what they are, to my mind, is less how militarily elite they were (a discussion which threatens to split a few too many hairs, I feel), but the circumstances of their respective creations and the duties they took upon themselves outside of direct warfare. That the Hospitallers ran hospitals (broadly speaking) and that the Templars ran banks (another generalisation) made those Orders relevant in ways well beyond the grasp of conventional military organisations. And that the Teutonic Order was "imperial", and tied to a specific cultural identity, again changes how we ought to consider it was both a medical and military order.

Sorry that I can't answer your question, and that there may not really be an answer to the question. But if you're looking for information concerning the broader relevance of these Orders, and others like them, then there's a lot to go off outside of direct military action (plus accounts of direct military activity).