Frankly, my answer is that it depends very much on the tone and content of this criticism. Because that is a very eloquent way to discern the true intention of whoever is making the critique. There's a difference between being rigorous, even blunt, and being plainly rude and insulting.
Criticism aimed to point out my flaws (and why not, strenghts) and help me to improve as a composer is welcome. Sometimes I'll agree with it and attempt to correct these flaws (or to build on these strenghts), and otherwise I might disagree (most likely on aesthetic matters). But I'll certainly learn from that.
On the other hand, criticism aimed only to discredit or to act out envy and jealousy must promptly be dismissed. I don't think Tchaikovsky found anything to build on from Hanslick's verbal abuse on his Violin Concerto, or that Rachmaninov thought that Cui was actually helping him when dubbing his First Symphony "a program symphony commissioned by Satan on the Ten Plagues of Egypt".
Listen to the critics - but keep in mind what Sibelius said: "I have yet to see a statue of a critique".