According to the building plans, the tower will rise to 1776 feet. However, it reaches that point only with the help of its uninhabited "needle" part, on top. Absent that, it's less than 1400 feet. Therefore, Chicago's Sears Tower will still take the prize for the largest inhabited building, if you include only the inhabited portion.
But even the Sears Tower won't hold that honor for long. Standing over it in the same city will be the Chicago Spire, which should be completed in a couple of years and stand at 2000 feet. So to recap, New York, will have the larges inhabited freestanding structure in the United States if you include even the uninhabited needle, the Sears Tower is the largest inhabited freestanding structure if you only count the inhabited parts, and the Chicago Spire will make all those arguments any way, dwarfing either of those--but being dwarfed itself by some TV towers, but which don't count since they're not inhabited structures.
Did you ever think the question of the tallest building was so complicated? Brace yourself: It gets more confusing if you start talking about the tallest in the world. Most sources that talk about the world's "tallest building" will point you to the TFC 101 building in Taiwan, which is almost 1670 feet. However, that again assumes you're talking about inhabited structures. The tallest of all "freestanding structures" is actually in Ontario: the CN Tower, which stands an impressive 1814 feet. But taller than either of those will be the still-in-construction Burj Tower, which will rise more than 2600 feet over Taiwan.
Why this obsession with being "the tallest"? It comes down to image and yes, to money. Any city that can boast it has "the tallest" building stands to bring in lots of tourist dollars, not just to that building, but to other businesses, as visitors make side-trips to businesses around the tall building. Thus, a visit to, for instance, the Freedom Tower will likely benefit restaurants and hotels around the structure also.
That's why you will continue to hear various cities laying claim to having "the tallest building," without spending much time or effort pointing out the fine print. And let's face it: Being home to the tallest TV tower just doesn't boost a city's image like being home to the the Sears Tower.