Ventless puts a huge amount of moisture into your home. Safety wise they have low oxygen cut-off, so I don't think that's a huge deal anymore. But I wouldn't (and didn't) buy them.
We installed a nice sealed unit with outside venting. It doesn't suck air from the house (it brings in outside air for combustion and vents externally through a single double-walled vent), puts out a huge amount of heat, and keeps the house sealed.