I don’t know if it would be a significant difference but yes white gas in a whisper lite would produce less moisture. It will also produce more BTUs at altitude resulting in less burn time. I used a whisper lite for many years. It is a great stove. Your breathing and perspiration will generate more condensation.
As far as using it in a floor less shelter, I would. I used to use it in the vestibule of my tent in bad weather all the time. One of the reasons canister stoves became popular is because the base doesn’t heat up so you can use it in a floored shelter. Alpine climbers do it all the time. Just use common sense.
The drawbacks to the whisper lite are weight, it needs to be primed, the possibility of a fuel spill, and the necessity of a fireproof place to set it up on. They also soot up the jet if not properly primed. But that is easily fixed. Now that my kids are showing an interest in the backcountry I am going to pick one up again. It works better for larger groups than the canister stoves and for longer trips, the fuel is cheap and found everywhere, and you can fly with it. As a plus the international version also uses other fuels.