For me, it would depend on what I wanted to do. I know that may sound like pussyfooting around the question, but sometimes I want to get my teeth into it (metaphorically of course). I did this while covering some cushions for my friend. She asked for covers, I took the old ones apart and used them as a pattern. The only reason being that I wanted to do it.
Other times I have just made a cover and left the old ones on.
There is nothing worse than having pulled the whole thing apart and then having to spend hours doing something you don't want to do!
BB