Both at the same time, but then I'm paranoid about these things. I usually have two tabs open on the computer (or two different devices), and then press the "buy now" button simultaneously.
Then I buy travel insurance immediately afterwards, followed by hire car, etc. All aspects booked and confirmed within 30 minutes usually.
That comes from living in a region rather than London, so flights etc tend to be very limited as to what flies from our local airport on what days, etc., so it's pretty fundamental to be certain I can get flights that match accommodation dates.
We never do hotels either, and often villas/flats etc are pretty hard to find for specific dates, specific locations, specific facilities, etc., so if we got a flight but then our preferred accommodation had got booked, we'd be likewise stuck and struggling to find somewhere else suitable for us.
The pickier you are, I think you have to do things simultaneously. However, if you've loads of flight options and don't really care where you stay, I think it's a lot easier to do things separately as you'll probably always find options that suit.