All "working" diesel engines with turbos, are using them nearly all the time, and are making power efficiently, so there are no big non-turbo diesels left, as they are too inefficient.
In theory, these small gas DI turbo engines should work the same , but are not so good in reality for some reason? Maybe they are made to game the EPA mileage test, but fail in real life with not so great 87 octane, so they want to ping, and then have to run super rich not to blow up?
I do find it interesting that the "big" 2.5 NA(all with AWD) in the Subaru family matches or beats these GM fwd SUV's in mileage, if not at the drag strip.