He can compare himself to whoever he wants. The problem is one of A don't necessarily equal B.
Yes he's arrogant. That's been shown through the whole campaign. It's just that people let it slide. Of course you have to have some arrogance to even run for the office.
Time will tell what his ability to handle the office is. What he's doing now is facing reality and the programs Bush implemented cannot be removed without sacrificing part of the security of the country.