Caesar has a tumor...it's probably affects his memory
Could be. However despite what his speech checks and such may suggest, the ending where he takes over the Legion certainly doesn't suggest a "sensible" leader. And seems to be the person that Caesar described to the letter.
■If the player sides with the Legion and allows Caesar to die of his brain tumor, Lanius will become the new Caesar. He is far more brutal than Caesar, and handles several things differently than Caesar would if victorious. For example, he would have Arcade Gannon crucified rather than keeping him on-hand as a doctor, slaughter the people of the Strip upon arrival at the gates of Vegas, have Chief Hanlon crucified with the other NCR Rangers rather than granting him a swift death out of respect, exterminate the Followers of the Apocalypse rather than giving them safe passage out of the Mojave Wasteland, and pursue the Enclave remnants rather than recognizing it as a lost cause.
I don't really like the Legion, and Caesar's not
much better than Lanius, but in terms of keeping it stable and coherent, Caesar is the better bet in my view.