Patton had a "Best Picture" Best Actor movie made about him. He came off as the best general ever, and his nemesis, Montgomery came off as a schnook.
Any WWII movies I've seen that included Montgomery have made him look like a schnook.
Rommel comes off as the worthy adversary, the tragic figure.

Now, from reading history:

Patton started the war as a division commander, took an army of recruits into combat with a tough foe, and managed to get victories. If he'd kept his hands to himself in Italy, he would probably have been "commander, Ground Forces, US Expeditionary forces, Europe. In true tragic format, he was not as tough as a truck.
Rommel was a "field marshal" but never had the resources to merit that rank. He got some early victories but when he faced organized opposition, he was routinely defeated. IMHO, Rommel was a good corp commander, and it might be an interesting exercise to speculate: What if Rommel was at Stalingrad and Von Paulus was in command of the DAK? He was not as significant a factor in the war as his "publicist" made him out to be.

Montgomery had ups and downs. El Alamein, Market Garden. His legacy seems a bit tainted, as Market Garden and Canne seem more to more than offset his desert victories. Montgomery was a schnook. Okay: He was a pompous schnook. When duty called, he answered. He was not a "great" general, but he was "good enough."

Patton is seen as the best general other than Eisenhower because Eisenhower prferred him over Montogomery. As you said, Eisenhower saw Montgomery as s shnook.

Now I see Montgomery as a rather exceptional general. His character may not have been likeable but his skills in the field of battle were good. I'm no expert but of course his desert campaign was exceptional and, despite what people think, Operation Market Garden was a relative success. 90% success in fact. yes, more live than expected were lost and we never got Arnhem but we got most of what we went for and the counter-attack afterwards helped us breakthrough. Montgomery got a bit greedy but the idea was genius and frankly worked. it was just shobby reconnisance (i forgot how to spell it) skills on his command side that really ruined it.

Now I will admit. I think that Rommel is very much a ruined general. But of course at the end of the day the victors write and history and Rommel didn't win. But his desert campaign went rather successfully, until of course Montgomery got him. And to be totally frank, other generals he was working with were very peculiar or stupid and Hitler was able to override any operations he didn't like. if anything, Rommel was really on the wrong side.

Montgomery, Patton and Rommel versus Chuikov and Zukov. Interesting