Victor, the problem with ANY generator is the noise they produce, no matter how loud or how quiet, they eventually become a nuisance and many sites either have bans on using them , or have strict time limits of use.
To the point of your post:
2 Stroke: Tend to be noisier than 4 stroke, use a petrol/oil mix, so tend to be smellier emissions, need very regular servicing and suffer more breakdowns in their lifetime, also, output can be more erratic than a 4 stroke.
4 stroke: tend to be quieter, use petrol only as fuel, so cleaner emissions, longer maintainence periods, output can be more stable than 2 stroke.
Cost to run:
2 Stroke,around 60p per hour plus oil
4 Stroke around 62 p per hour
both tyoes,add servicing and repairs, plus,remember to allow the extra weight when calculating van loading, including carrying petrol, in the car or van.