Totally agree with what people have said about mats and warmth, but in my one experience of using a bivi, warmth was exactly the problem.
I was solo walking in the Pyrenees (perhaps a bit silly actually) in September. The problem was that although the storm I got caught in was severe, the temperature was very warm, i.e. the sort of sticky warmth you only really get in a storm. The bivi bag was a hooped, gore-tex, expensive ... type but the goretex was totally unable to deal with the heat generated inside the bag. In an attempt to relieve the heat, I had to open the bag slightly, but the rain was like stairrods, so I had the choice of holding the opening in such a way that the rain wouldn't get in, or sleep. Not a great choice to have to make.
I would imagine that in cooler climates, perhaps the bivi bag may have it's place, but since I spent many nights in my teens, including wet ones (if you're sniggering I mean rain), under a 'tarp', it's unclaustrophobic nature is great by me.
S.