It's been awhile since I've read the novel but wasn't only NYC targeted in the attack at the end?
The alien was teleported in and it sent out brainwaves to people on the planet with images that the aliens were going to invade and that the should be as ready as they can be for it.
As for the movie, Adrian made it look like Manhattan was the culprit and that multiple cities were targeted to make sure that any country would think it was their enemy that cause the attack. Since they knew what Manhattan can do, people feared at what he might do in the future. With Manhattan as the enemy, they could connect to him in a way that an alien would not because they know for certain that Manhattan is a real entity rather than some fictitious alien that only has a rotting corpse.
I can see why they changed it but I don't know whether or not there is any proper way to measure what each different outcome would impact the world, imo.