Faster data speeds mean that it's much easier to consume data, especially when viewing video and using FaceTime for video chats. That's a concern for Moore, who said he now plans to better track his data usage so he won't blow past his new monthly Share Everything 2GB data plan. Otherwise, he'll have to pay an overage charge.

Moore gave up an unlimited plan with Verizon to get the new iPhone 5, which he likes for its Siri turn-by-turn directions in Apple Maps and its larger 4-in. screen.

Using a Verizon app, he found out he'd already used 200MB of data in just four days. "I was surprised I had used that much," he said.

Analysts note that data speeds are highly dependent on how many LTE smartphones of all types are using a nearby cell tower, as well as a user's distance from the antenna. All of the major U.S. carriers have for months sold smartphones and tablets running Android that use LTE, so those will be competing with the iPhone 5 for wireless network capacity.

Also, some cities on certain carriers in the U.S. don't even have LTE, which stands for Long Term Evolution. Verizon Wireless covers the most cities -- nearly 400 -- of the U.S. carriers. , but also has fast HSPA+ speeds across the U.S. Sprint expects to reach 100 cities by year's end.