Metro Vancouver studied this and found that when transportation costs were factored in, car reliant outer suburbs became more expensive than "pricy" downtown and inner suburbs.
http://bc.ctvnews.ca/suburbs-pricier-than-vancouver-when-tra...
That's not quite enough to support the blanket statement "living in the suburbs is not cheaper than living in a city."
As someone who's in this situation right now, I can guarantee you that moving out of my city is the frugal option.
The reason is for this is because many of these suburbs are wholly designed for the car and that's the only viable transportation option for anything and the car is the most expensive form of transportation.
But most of the major cities that I've been to in the US don't have a decent public transportation system. If they would fix this, then people could become less reliant on cars.