The glorification of self were the base of the similarities between Hitler and Mussolini. Both leaders asserted that they, and only they, were the man for the job of leading their respective nations out of the mire of a post World War I world. Their personalities were driven out of the need to provide a vision of unity and symmetry that was craved by their people. Both of them were extremely charismatic, what Clive James would call "the Charisma Kids." They both understood that political ruling involved a public relations aspect, and both ensured that their PR machines were able to disseminate their message and consolidate their own rule at the time.
Both were talented speakers, Adolf Hitler especially. He could motivate a crowd like almost no one else of his time, pushing exactly the right buttons to incite them into a frenzy of cheering and support. He was also paranoid, felt everyone was out to get him (perhaps one of the three dozen assassination attempts against him might have pushed him over the edge). He had the capacity for both extraordinary kindness to children, animals, and women, and then flew into fits of incredible rage and cruel indifference.
Mussolini was arrogant and pompous. He believed he was the new Roman Emperor, even though his empire never came close to rivaling Ancient Rome's on any level. He was a notorious womanizer, and was loud and boisterous at parties, yet pensive and brooding in private.