I think Vivien makes a really good point about the importance of dialogue in a critique. I like to know what someone is going for, what level of criticism/ reaction they want. For example, some people are perfectly happy with, "Wow, the emotions in that piece really spoke to me." Period. Others are going for something more like, "You matched the flow of the writing with the emotional intensity really well; the sentence structure became short and choppy when the protagonist was frustrated, long and lyrical when he was lost in a romantic reverie, etc. The one point this really broke down, for me, was the end. The short and choppy sentences may have meant to convey heightened emotions, but they were jarring and artificial to me, and took away from the excellent story you were telling."
(That is totally made up.)
My B.A. is in English with an emphasis on creative writing, and I was lucky enough to have some truly stellar professors who guided us in how to best give (and receive) constructive criticism, and I really enjoy it. But, to get back to Vivien's point, if someone is looking for the first response and I give him or her the second response, it can get ugly.
So I try to ask a lead-in question or two to get the lay of the land, and go from there.