There is no such thing as a "Ventless Exhaust". There are self venting range hoods that are very common. A self venting hood will not vent to the outside of the house but back into the kitchen. There are special charcoal filters that are used in this setup. I prefer to vent to the outside of the house, however there are some good arguments to be made for venting back into the room. The first is that you do not need to have a vent to the outside installed, thus you may save some money on that installation. On the other hand the charcoal filters will cost a little more to keep maintained. Another reason to vent back into the room would be for the efficiency of your heating and cooling. You can pull a great deal of air through your exhaust fan.
The reason I like a hood that vents to the outside is because I am tall and when I turn a self venting range hood on it is usualy blowing right at or slightly above my face.
A recirculating fan doesn't eliminate the moist air from cooking. A fan that vents outside gets rid of the smells and the moisture. You'd be surprised how much damage and mold occurs from all that extra humidity from boiling spaghetti