Good analysis in this post. Sometimes I don't know how Ike survived with his sanity having to deal with George Patton and B.L. Montgomery, prima donnas supreme but both, in their own way, great generals, in the same war.
I would hardly consider Montgomery to be "a great general" in the same way that one would call Guderian, Rommel, or MacArthur "great".
Montgomery, tactically, knew only two moves: the straight-ahed thrust to fix the enemy, and the hook behind his flank, and neither without obvious superiority in men and weapons. Alamein was not so much a great victory of British arms as it was Monty being able to take advantage of a Rommel at the end of an extended supply line and with practicaly no tanks.
Whenever Monty took on Rommel in anything approaching an even fight, Monty came out on the short end every time. I will not even get into the debacles at Montgomery's hands concerning Sicily, Caen, and Market-Garden. Montgomery, despite his strengths as a command (great organizer, beloved, fighting spirit), was a creation of the press. He was a lousy tactician.
As for Ike keeping his sanity, I even call that into question. After the Normandy landings, Ike had two options in taking the fight to Germany; the broad front (which would entail huge numbers of infantry which were not available and cause all sorts of supply problems), or the narrow front (a strike straight into Germany by a thrust of concentrated armor).
When faced with this choice, Ike punted. Because to favor one general (Monty or Patton) or approach over another was too difficult a choice to make, apparently. I always thought that a general's job was to shorten the war by making the enemy pay as quickly and efficiently as possible, with as little loss to his own army as practicable. Apparently not.
He opted for the broad-front approach and lengthened the way by ensuring supply difficulties and a lack of concentration of force in places where it would have done the most good. This approach led directly to the misery of the Hurtgenwald fighting (3+ american infantry divisions chewed up -- over 100% casualties -- for nothing), which then begat the Battle of the Bulge (the Germans attacked the thinned-out Ardennes sector, from which troops had been pulled and fed into the Hurtgenwald fighting).
Ike deserves every credit he gets simply for preventing Patton from strangling Montgomery and vice versa.