"There's no question the Giulia is the sports sedan in this comparison and the Stinger is the grand tourer. "
Exactly as conceived, designed and carried out. You should know what kind of car you want.
"Despite the larger hardware, the lighter Giulia out-stopped the Stinger in 60-to-zero-mph testing, stopping in 116.9 feet versus the Stinger's 119.2 feet. That's far from the end of the matter, however."
No, that is the end of the matter. They proceed to compare on the track, lapping to see what the brakes do upon sustained demand. The Alfa "could be" a track car. The Stinger never was or will be a track car. Less than three feet in a 60 to 0 stop test is nothing. In the real world of touring/traveling, and daily driving, an emergency stop is all you need. And the brakes in these two cars stop the car quickly and safely. The brakes in the larger, heavier Stinger don't need improvement, unless you are going to track it (for fun).
"The Stinger's best lap took 1:52.48 versus the Giulia's 1:55.53."
They complain about the brakes on the Stinger, but isn't lapping faster what it's all about? You don't feel "confident" in the Stinger when braking compared to the Alfa, but the Stinger works? Isn't adaptation to what the car is what marks a better driver? You don't always get the "feel" you want, but if you can lap faster you say "I'll take the faster car". Nothing else matters.
Bottom line: the Stinger concept is a high performance, luxurious, comfortable, utilitarian gran turismo with 70s retro design chops; far more car for less money. It wins. To get close with an Alfa you have to spend twenty grand more. Even then it won't compete as a gran turismo, it just outperforms the Stinger on the track.