Patton and Rommel had a series of near-misses, but I don’t think they ever really faced each other in a capacity that can be used as a reasonable head-to-head comparison.
By the time the Americans closed against Axis troops in Tunisia, I think that Rommel had essentially been pulled from the theatre, somewhere around May, 1943, first for physical ailments and then because it was plainly apparent that North Africa was going to be lost to the Allies. Rommel was stationed in Northern Italy while Patton was invading Sicily. Then Patton was sidelined for the slapping incident, and Rommel was transferred to the West.
During the beginning of Normandy, Patton spent the initial part of the invasion in Southern England threatening the Pas-de-Calais with his fake army. Rommel was serverely injured on July 17, 1944. Patton commenced Operation Cobra, the breakout of the Cotentin, on July 25. Rommel never really commanded thereafter, and was dead by October.
I’d like to do a detailed comparison of the careers of the two, but I haven’t the time. Perhaps someone else can flesh this out and check my facts. Going from memory:
World War I
Rommel: Extensive combat experience throughout the war on all major fronts, I think. I know for certain that he was effective in executing the storm-trooper style of penetration and bypass of strongpoints exhibited by the Wurtemburg Mountain Battalion, and personally commanded a highly successful assault which won him the Pour le Merite.
Patton: Commanded part (maybe all?) of the fledgling American Tank Corps. Was “shot through the ass” (I think that’s his own words) in one of his very first engagements, although he had time to chat with Douglas MacArthur on the battlefield.
Interwar
Both suffered from lack of promotion in the interwar years, so that at the outset of hostilities for their respective countries, I think that both of them were of fairly junior command rank (both brigadiers, perhaps?). Both spent a fair amount of time training young troops–Rommel ran a cadet school and Patton a tank tactics school. Both were outspoken proponents of the offensive capability of tanks on the battlefield. Rommel actually wrote about it, and by most accounts, Patton was well aware of Rommel as an author before he (Patton) ever fought in WWII.
WWII
Both were promoted quickly after the commencement of hostilities for their respective countries. Both executed about three major campaigns, I think. Rommel: France, North Africa, Normandy. Patton: North Africa, Sicily, France and Germany. Only Rommel had what could be considered independent command. Both sat out considerable portions of the war, Rommel due to ill health and injuries and non-combat assignments; Patton due to ill behavior, politics, and non-combat assignments.
Both were arguably held in higher regard by their enemies than by their allies during the war. The Germans purportedly considered Patton the Allies’ best commander while Montgomery and Bradley had personal reservations about him. The Allies had a very high regard for Rommel while some of Rommel’s superiors thought him to be too young, rash, and inexperienced for the level of command he attained (“Marshal Bubi”).
I don’t know. Does that look like an accurate comparison to you? I’d sort of like to get it right for the purposes of this conversation, so tear it apart if you see anything wrong with it.