I agree with "sullymonster" that Caesar would be more of a Donald Trump type to me. He would be a great real estate mogul!
I'm laughing about the Dick Cheney thing for Cassius. Dick Cheney and the word "seduction" are words that just do not go together LOL!
I don't know about politician for Caesar. I picture him as more of a Donald Trump type. Trump did, after all, came, saw, and conquered - and he is still doing so. Consider this quote as well: "It is not these well-fed long-haired men that I fear, but the pale and the hungry-looking." That also sounds like Trump to me.
I completely agree that Brutus is a "Mr. Smith", with a slightly more violent edge.
Consider this analysis of Cassius from Enotes: "Statements Cassius makes, particularly during the "seduction scene," suggest that his motivation for initiating such a plot is a combination of political ideology and personal envy." Sounds to me like Dick Cheney!
This is a great question! Undoubtedly, Caesar would be a politician. Given his reputation with the women, he'd probably be like Bill Clinton, but Caesar would never deny his affairs. He'd feel entitled to do whatever he wanted.
Brutus would be like the title character in the movie "Mr. Smith Goes to Washington." He's a bit naive and believes that everybody's motives are pure, just like his are.
I need to think about Cassius a little more.
Big question... I think one way to approach this would be to pick current politicians such as Barack Obama, John McCain, Hillary Clinton, etc. and think about Caesar etc. in that context. Focusing on the political/leadership angle would be a good way to get started, and you can use modern characters to show similar character traits in today's times.