This is a great question. I am sure that people will differ in how they view both honor and pride. In light of this, let me offer a few perspectives.
First, some characters in the play are predominately arrogant, that is, proud. Cassius is such a one. He does not believe that Caesar is great. He points to his weaknesses and his falling sickness (probably epilepsy). He also believes that he and his friends are just as great or better than Caesar. So, why honor Caesar? He is just a man.
Second, some characters are more honorable. Such a character is Brutus. On the one hand he loves Caesar. He sees his kindness and clemency. However, Brutus also loves the Republic. And a part of him believes that Caesar is too ambitious. So, he is torn. In the end, he decides to join the conspiracy, but not out of a sense of pride but for the sake of the Republic. This is very different. Honor motivates him. Most will say that he acted wrongly, but his motivations were honorable. This makes him tragic.
Third, some characters are both honorable and proud. Caesar fits this category. He does not heed the many signs of his impending doom. Pride blinds him. That said, when his will is read after he dies, it is clear that he loved the people. He was a man of honor.
What makes Shakespeare a great writer is that all of these points are debatable.