Although the Katrina disaster dwarfs the collapse of two buildings in many ways, the perception of the impeccably way the aftermath was handled may raise the esteem of Guiliani in many minds.
You have stated it correctly.
The one crucial point between 9-11 and Katrina is one was a premeditated, vicious sneak attack to decapitate the nation's political leadership & center of global trade.
On the other hand, Hurricane Katrina had already slammed through southern Florida and was clearly visible as this storm entered the Gulf of Mexico and began heading in the general direction of New Orleans.
Rudy, in the midst of NY & America under multi-terrorist attacks, reassured the citizens of New York, the nation as a whole, and even the world.