My apologies Fujative, I did not realize the Sport meant it was a smaller version of the Outlander. I thought it to be simply a trim level until I looked today. It is actually slightly smaller than the Compass, with a slightly longer wheelbase.
However, the Mitsubishi and the Compass share the same basic frame and basically the same engine. The frame and engine were co-developed between Chrysler and Mitsubishi a little while ago, with Hyundai being a partner for the engine as well.
That being said, by the time you load up an Outlander Sport with some of the same features as the baser level Compasses, you have a more expensive vehicle. Mitsubishi's incentives also aren't quite as good as Chrysler's. However, the one good thing about Mitsubishi is their warranty: 10 years or 100,000 mile powertrain (vs. 5 year/100,000 on the Jeep) and 5 year or 60,000 mile limited warranty (vs Jeep's 3 year/36,000 mile). You tack on the cost of a service contract from Chrysler to meet the Mitsubishi's standard warranty, and there's most (if not all) your cost difference right there.
I still love my wife's Jeep, and although she doesn't dislike the Outlander, she'd never trade her Jeep in for it. However, I do suggest others test drive the Outlander Sport and research it before making a purchase, it is a worthy contender against the Compass.
2012 Jeep Compass Sport 4x4
2.4L I4, CVT II, Freedom Drive I
2010 Dodge Dakota Quad Cab 4x4
4.7L V8, 545RFE, Big Horn Edition