Hmm, his greed feels like the most obvious choice. He's obsessed with gold, money and treasure, and that's a key trait in every game and series he's appeared in.
His strength and brutishness is up there, though moreso in Wario Land than WarioWare. Weirdness is there too, but that's mainly about his world/series rather than him in particular.
The biggest thing that sets Wario apart from Mario even more than his more thuggish traits, is that Mario is very reactive. His stories are driven by wanting to help others in any given situation.
Wario meanwhile is entirely driven by his own desires, which can one way or another, always be drawn back to greed. Wario wants something, he takes initiative to get it.
Shake It in particular does a wonderful job portraying that. He could care less about the captured princess or terrorized world he's being told about, but the moment a possible reward that satisfies his greed is on the table, he's right on it, with all the good he does in the process being entirely incidental.
I always preferred when Wario is portrayed as stronger and more brutish, and yet greedy at the same time, if I said my thoughts it would just repeat what has been said. Wario Land games always felt best to me whenever it felt like a seperate game. Wario goes into different realms often, the mystery and the lore intrigue me. Wario's need for gold and power is also something I love. he's a perfect charater.