Julius Caesar above all is ambitious. He is a master manipulator. Does he want to be the first Roman emperor? He does. He manipulates the crowd by refusing the crown offered by Mark Anthony. Is it a set up? Of course. He knows that the more he says no, the more the people will want him as their leader, forgetting, of course that Rome at this time is a Republic, a representative form of govenment. They do not realize that they will be giving up their rights if they make him their supreme leader.
One of the clues to this man's character is how he speaks. He uses an imperial tone. For example instead of saying '"I will go forth today." he says "Caesar will go forth today." In his mind, he is already emperor.
A tyrant? Who knows, since we never get that far. Brustus fears that he will be since total power is an awesome responsibility and if we look in history, the old saying, power corrupts and absolute power corrupts absolutely, is true.
Is he sympathtic? To a degree perhaps but it is hard to be sympathetic to an arrogant man and Caesar is arrogant.
The bottom line is that he is a human being and flawed.