If it's just a microwave, I see no reason to vent it outside, like most of the rest. I don't think most microwave ovens are set up to vent anywhere other than the general open air.
If it's a combination microwave and range hood, it would certainly be preferable to vent it outside due to the range hood functions. Recirculating the air inside from the range hood is decidedly inferior. The grease filters do trap some of the grease, but the moisture still accumulates. A stovetop tends to produce more moisture than microwaving, both because of how it's often used (boiling or simmering stuff) and because the combustion of the propane produces water vapor as one of its primary emissions, along with carbon dioxide.