From what I've seen by looking at the experiences of Compass owners with the 2.4 and Caliber owners with the 2.0, it looks as though there is only one situation where the difference in fuel economy is substantial: the EPA's fuel economy test. In the real world, there doesn't seem to be much of a difference.
In my opinion, powertrains can be designed to do well in the EPA test - with little or no benefit in mileage when applied to how people actually drive their vehicles. For example, hybrid vehicles never seem to achieve the stratospheric EPA ratings that are advertised. However, none of us consistently run our vehicles in a lab, with precisely set temperatures and driving cycles.
Don't get me wrong - for comparison purposes, the EPA ratings are the best thing we have...and when looking at differences of 7 to 10 mpg, I personally feel they're meaningful. But then you're looking at differences of less than 3 to 5 mpg, it's difficult to use this as the "acid test" of whether one vehicle will actually use more or less fuel than another.