Reasonably quick to get going. Not very adjustable. Great in sub-zero temperatures and at altitude eg mountaineering. Primus - runs on parafin. Needs to be primed with meths.
Fuel is readily available in most places and relatively cheap.
Camping Gaz - runs on proprietary gas canisters. Main pitfall is miscalculating the number of gas cannisters needed for a long trip and not being able to get replacements in remote areas. Cheap to buy, expensive to run. Trangia - runs on firelighters. Not quite, but nearly true.