I like the newer Buick cars although I always wonder why someone would buy a new one over a new Chevrolet. A Buick Verano is a rebadged Chevy Cruze, maybe a bit more rear seat room, but higher $$$ and less MPG. The LaCrosse is a rebadged Malibu, again for much more $$$ and the Malibu is a better car.
I see that the Buick Encore uses the same 1.4L turbo engine that the Cruze uses. So far my Cruze has been pretty decent, it's quiet inside and gets pretty good mpg, 34.4 overall on a trip to Cleveland back in April, and 35 even on my August trip to Cleveland, and that includes both highway and city.
I would guess that the Encore, being a bit bigger, less slippery, wouldn't get the same figures though. So the Mazda wins there.
Me personally I would take the Mazda. But I'm not a big fan of CUV/SUV's