Owning your own home

Flat roof, new bit of building, I'd say definitely warm. Warm roof means the structure (which is likely to be timber? Unless you've got a grand project in mind) stays warm under the insulation, which means you don't get condensation in amongst your timber structure (not something you want). And less risk of cold spots so less risk of condensation on your ceiling and generally less heat loss.

If you're going for a concrete roof structure you could consider an 'inverted' warm roof, which just means top to bottom it goes ballast (soil, stones, paving etc), insulation, waterproofing, structure. Instead of waterproofing, insulation, structure. The waterproofing and insulation are swapped around, the advantage is that the waterproofing is protected from extremes of weather etc. Some other wierdness can happen with the layering (cold rain getting to the waterproofing), and really it's only good on concrete because you need all that ballast to stop the insulation blowing away.

Not sure there's ever an advantage with cold flat roof, you need a ventilated void in there which can be a problem with extensions (flat roofs vent round the edges, so easier if they are 'free' edges not up against a building).