Great discussion.
Critiques I've received in the past have been too consistently soft and encouraging. Since then I've taken some strange artistic directions that will probably call for more specialized critics. Overall, I've had better luck measuring myself against composers, songwriters, authors, and artists from other disciplines—my heroes. I also seek new perspectives by reading, watching classes, listening to lectures, and so on. It's a boon.
When I do seek an outside perspective, usually it's because I want to make sure that a particular image or idea is actually getting across to the listener. Sometimes it's easy to accidentally leave out a crucial, small detail that leaves your audience baffled about what's happening in the narrative.
I do enjoy critiquing others, because it offers a chance to climb inside of another person's song for mutual benefit. There are myriad different ideas about songwriting as an art, and then there are all the differences in life experience, techniques learned, genres preferred... every songwriter's got unique sensibilities. Tunesmith's comment stands out for me here: it's important not to think exactly as though the object of critique is your own work. They're writing their song, not yours, so you've got to be somewhat sensitive to the context of what they've written.
As a teacher, I work to understand a wide array of perspectives and approaches; that way I avoid subconsciously trying to turn my students into clones of myself. As a student, I try to analyze different voices, new methods, new perspectives on the art. Critique improves me on both fronts, and allows someone else to potentially benefit also.
Oh, and if a person is more obviously at a beginning stage of the process, I may recommend them some reading. Certainly I get more specific relative to how impressed I am by the craft behind the song.