Writing is often taught by showing examples of bad or mediocre writing and asking the students to critique and improve on it. Similarly, in writing workshops you learn by having others critique your work, but also by critiquing the work of others. This would suggest that these are at least partially the same skill: I know that on occasions when I've read someone else's text and pointed out things that could be improved in it, I afterwards end up also being more aware of those things when writing something of my own.