What is safer, a "white gas"/coleman gas or a propane stove to use inside a camping trailer.?

OK. The gas stoves using coleman fuel, if lit properly, are the same as propane in terms of safety. Propane will be easier to use. I prefer the older gas models but I collect coleman and that's what I like.

If it's a tent trailer or an older model canned ham and there was no stove that came with it, that is a clear signal that YOU DO NOT COOK INSIDE YOUR RIG! there's danger will robinson in carbon monoxide from Colman fuel stoves or propane. For camping economics the liquid fuel stoves are the cheapest. The easiest to use would be the propane. trade offs to both my personal choice is propane as it is on the safer side to use and more gizmo's are made for it as well.

Cook nothing inside, unless in extreme circumstances. Not only is this a fire/explosion hazard, but your stuff starts to smell rather tasty to the critters. Critter encounters don't always end with a smile.

The propane is probably the better choice to use indoors. The white gas stoves burn very inefficiently until they heat up to operating temperature. They give off a lot of fumes and high flame when you first light them. The propane stoves do cost more to operate, but you don't spill fuel while refilling it. Edit: I stand corrected you should not use either in a confined space without the proper venting.