You are always taking the chance of carbon monoxide poisoning when breathing vent gases. If the flame burning changes, you can be made ill. If you have had no problem with moisture from the other unit, that informs that your house is loosely built so there is a high air exchange; it is one reason for high fuel bills. One can not burn a vent-free unit long in a new construction as they are very tight and would feel wet in a short while. If you have a choice, seal the air leaks in the house, add insulation everywhere possible, so you can live safely.