On top of that: Who would he butt heads with the most, in general?
This question excites me, because Ohio University (where I go) has the original papers of Cornelius Ryan, a famous journalist in World War Two who wrote the Longest Day.
In this collection is his interview with Eisenhower, where he describes British General Montgomery as "psychopath" due to his unwillingness to admit mistakes.
And if I were to add on to this, Eisenhower was one of the only famous generals who did not see action in World War One, and apparently this led to a lack of respect.