The new tower was expected to rise higher than the old landmark's 1,250 feet Monday.
The owners said they'll try to take observation deck business from the midtown skyscraper and win the business of some of broadcasters that send signals off the Empire State's antenna, the New York Post reported.
"We're looking to maximize revenue and maximize the reputation of 1 World Trade Center," said Douglas Durst, who is building the tower in partnership with the Port Authority.
The Post said the antenna business could bring in $10 million in revenue.
Port Authority officials say the new tower's observation deck will feature more than the small gift shop at the Empire State Building. An outside firm will design, operate and market the new tower's observation deck.
The Port Authority lost antenna business when the World Trade Center towers were destroyed in the Sept. 11, 2001, terrorist attacks that killed nearly 3,000 people.
The owners of the Empire State Building declined to comment on 1 World Trade Center's plans, the Post said.
"The world's most famous office building, the ancestor of all super-tall towers, welcomes our newer, taller cousin to the skyline," the Empire State Building's operators said in a statement. "We've watched you grow, and now we salute you."
The New York Daily News said Mayor Michael Bloomberg spoke of 1 World Trade Center Sunday.
"It's wonderful," Bloomberg said. "It's taken a long time. This is probably the most complex construction site in any place ever. I think what we've shown is that democracy works."
The tower is scheduled to open in late 2013 or early 2014, meaning it will have taken about eight years to build, and is to rise 1,776 feet with 104 floors. It is estimated to cost $3.9 billion.
The News said the Empire State Building was completed in 1931 after a little more than a year of construction.