Both forms are simply different syntactic choices to express the same idea, of which there are many to express this idea. More importantly, my question would be: How many times are you telling the reader about someone's breathing, regardless of the syntax you use to express it?
Exactly. Empty action for the sake of it is tedious to read--I would know, since I do it a lot. It's one of the biggest problems in my writing. It's easy to try to fill a pause with "he smiled," "she sipped her beer," "I closed my eyes a moment," etc etc. But chances are those actions aren't actually contributing anything. You need to determine what is actually significant body language and what is just filler. It's not always an easy decision to make, either.
They are really not quite the same. 'Took a deep breath' means one breath, as in a short calming or preparatory action. 'Breathed deeply' is a less determinate, more ongoing action, and could be brief or go on for a period of time. Either one is clearly fine to use in a suitable context, and there is no rule for how many times you can use a given phrase in a passage of a given length. Do you really expect anybody to give you an answer like 'you may repeat yourself five times per 10,000 words'?
