Rommel was retained in the post-WWI army. He was never a policeman or considered emigrating to America.
Despite his closeness with Hitler and Goebbels, Rommel was never a Nazi party member.
There is a lot out there about El Alamein, but the Cliff's version is that Rommel was at the end of a very extended supply line while Monty did what he does best, he took a very long time to stack his line with reinforcing units and supply stocks before launching his attack. Despite all the criticism we level at him, he really was a master of the set piece battle.
Monty was probably a good chess player.