[Cthulhu_]

I think the differentiating factor, for me, if I were in a hiring position, would be that full-stack engineers are curious, flexible, and both eager and very able to learn.

Specialists, I have less experience with working with them though so take these generalizations with a big and hopefully non-insulting grain of salt. On the one hand they will be experts in their field, know whatever they work on inside-out, and can squeeze every last grain of performance out of it - good DBA's are worth their weight in gold, they can solve a company's performance problems and save them millions depending on the scale.

On the other you have a group of people that sorta know one language, like Java, and will just coast along on it for their careers; their CVs will look impressive, their skills will be indistinguishable from someone who has one year of experience. I've literally seen code that was a copy / paste of the first google search result of "java sql query", buried ten indentation levels deep, in a critical core codebase.