As Liverpool, I could never beat Middlesborough and Arsenal. Middlesborough would always get dominated throughout the 87 minutes, the game would seem to be a draw and than someone would score and it usually would turn out to be Gareth Southgate. It was rather frustrating, never had trouble with Chelsea though.
My Man United team beats Chelski like they were a bunch of schoolboys. I've had 5-0 (FA Cup Final), a 4-1, a couple 2-0's.
I beat them with DC United and Man City and Portsmouth. But never had much luck when I was managing anyone else.