To echo what Richard III said, Monty was overrated. He wasn't horrible, just overrated.
El Alemain: Won a setpiece battles. However, he let the Afrika Korps retreat, and he did not pursue that aggressively.
Sicily: Got held up, not entirely his fault I believe. However, Patton did go around the obstacle and beat him to Messina.
Normandy: He did not quickly enough expand his beachead. Caen was supposed to be taken on the actual D-Day. While this could be considered over-ambitious, Monty's post D-Day offensives failed to take it any time to make a difference, and he failed to break out of Normandy. It took St. Lo and the 1st and 3rd armies (3rd was Patton's by the way

).
Arnhem: Seems to me an overly complex operation, though I do not know that much about it.
Ardennes Battle: Weaseled his way into taking command of the 9th and 1st US armies away from Bradely. Ordered withdraws from important locations (particulary St. Vith) in order to "tidy up the line." St. Vith was a road hub of near equal importance to Bastogne, and continued defense there would have held up German operations in the northern half of the bulge.
Rhine: Was supposed to breach the Rhine, but Patton beat him to it.
Now for Patton:
North Africa: Re-trained what I think was II Corps after the disastrous battle of Kasserine Pass (not fought under his command). Beat up on the Germans from the east.
Sicily: Took the long way to Messina, but got their first. However, the move was as much political (for his own glory) than it was military. He was actually disobeying orders.
France: Generally good chasing and routing of the Germans after the breakout at St. Lo. Utilized tank formations combined with close air support. Sound familiar? The closest American armies came to the classic Blitzkrieg. Became bogged down, I think in Alsace-Lorraine, due to supplies and muddy conditions. He's great for Blitzkrieg, but not for slugging matches.
Ardennes: Very well executed manuever of sending 3 divisions to cease attacking, turn 90 degrees to the north, and relieve Bastogne.
Rhine: First across I believe.
Govenor of Bavaria: Let's just say this was not a highlight of his career.
