They're identical. Aside from a few cosmetic differences, under the hood and inside they're exactly the same. Cycle wise, the Kenmore has Sani-Rinse as an option, but I doubt that would be used in testing.
For some reason no one, primarily Consumer Reports and other review sites, wants to accept that Kenmore has NEVER manufactured a single appliance. They are ALWAYS contracted and built by another company. Whirlpool has held the majority of their laundry machines and dishwashers, though a few have been manufactured by Frigidaire, GE, and LG. Yet still, Kenmore accepts numerous awards for "best appliance manufacturer" all the time, and gets praises from CR constantly.
This bias towards Kenmore has been going on for decades, though I haven't the first clue what the fascination is. My grandfather has a few CR issues from the 80's, and of course the Lady Kenmore belt-drive washer outscored the Whirlpool Imperial belt-drive, and they're the exact same machine. I adored my grandmother's Lady K, especially the solid state electronics, but learning that it is nothing more than a relabeled Whirlpool only made me respect WP more, not Sears KM.
Don't get me wrong, Kenmore is a great brand. Because they contract the best performing appliances from each respective company, you are literally getting some of the best that manufacturer has to offer, as long as you're not getting BOL machines. I have a couple of Kenmore machines, and I love them, but I know who the company is underneath that shiny Kenmore badge, and that was the only reason I willingly purchased them.