Bagels are a whole different ballgame, you can't find a decent bagel in the Bay Area.
But pizza? Your typical place in New York isn't a whole lot different from what you'd find at New York style places (e.g. Escape From New York, Serranos, Arinell's). The 99 cent chain isn't as bad as folks make it out to be IMO.
Out here you've got plenty of wood fired places 'authentic' and not (e.g. Zuni, Tony's, Una Pizza Napoletana, Pizzaiolo); Indian (Zante, Brother's); California (Zuni again, Goat Hill, Arizmendi / Cheese Board -- their sour dough puts puts anything I had in New York to shame); deep dish (Little Star, Patxi's, Zachary's); and, of course, Delfina.
The typical New York pizza isn't significantly different in overall quality than the stuff you find in the Bay Area. If you go looking for it you can find excellent pizza in New York I'm sure (but the same is true in the Bay Area).