Eh, both seem equally prone to sudden betrayals and being shot in the back.
But I think I would have to go with the Jedi Order. Of course, things get a little more complicated if we take into the expansive and now non-canon EU, so I'm just going to stick with the new, smaller, and thus more consistent canon.
On the whole though, I actually think it is the Jedi who have more influence and power. The Spectres, despite given near Carte Blanche, are still servants of the council. They must receive their missions from the council and when they stray too far, can be disowned and stripped of power. Jedi by contrast seem to be separate from the Republic, but in alliance with it. Prior to Attack of the Clones, the Republic appears to have had no standing army and delegated all peacekeeping responsibilities to the Jedi.
While the Jedi code clearly establishes what the republic might expect from their peacekeepers, that is still a tremendous amount of power to have contracted out to a third party. Similarly, by Revenge of the Sith, Mace Windu seems to remark almost out of hand that the Jedi would have to take control of the Senate once Palpatine is deposed, indicating they either have the political clout or military might capable of a rapid coup. Lastly, unlike the Spectres who are beholden to the Council, Jedi affairs seem to be able to be handled completely internally as evidenced by The Clone Wars, where
, a commissioned officer of the Grand Army of the
Republic, supposedly murders a suspect in GAR custody on a military base, yet can't be touched by the courts until said Jedi his expelled from the Order.
As for a one on one fight, it all depends on the individuals. Shepard can take on whole platoons, but Obi Wan has no problem jumping into the the thick of the enemy army to confront Grievous. Similarly, Jondam Bau can be strangled by a lone human, and nameless Jedi can be easily gunned downed to heighten the drama. Spectres are chosen from the best, while Jedi skills are cultivated from childhood. The fact that combat is not not the sole purpose of the Jedi, but more of an afterthought up until the return of the Sith I think gives the advantage to Spectres in general, but again, it all depends on who is fighting who.