It'll be Steinbrenner's decision (not Cashman's). They probably bring him back but they will have to pay him top price or very comparable to the top offer. The one thing we have learned is that these players rarely take a discount. I also recently learned that Judge grew up not far from the Bay area and was a huge San Francisco Giants fan as a kid.
The Yankees have a history of keeping their guys. In that respect, they are very different from the Red Sox who lost: Lynn, Fisk, Boggs, Clemons, Vaughn, Betts, and probably Bogaerts. The Yankees usually keep their homegrown stars like B.Williams, Jeter, Rivera, Mattingly. Maybe I'm forgetting some contrary examples--this is just off the top of my head.
As far as Cano goes, I wouldn't be surprised if Cashman knew that Cano was a steroids guy and that mitigated the Yankees interest in matching a top offer. In contrast, Judge doesn't have any skeletons in his closet and so the Yankees will probably resign him.
Cano is such a disgraced player, a guy who may have been on a HOF track due to his production at 2b But now he will get so few votes in his first year of eligibility that he will be off the ballot after his first year.