I believe it is a matter of the quantity of gas. When you roast in your oven for several hours, you use relatively little gas because the thermostat maintains the temperature with the gas flame very low (the flame will go up occasionally to maintain the target temperature if you open the door. With gas logs, you are consuming a lot of gas -- the flame is always fairly high, for 2 reasons -- to provide heat and to provide a cozy ambience. In a ventless gas system, there is a risk of degrading the quality of indoor air by lowering the oxygen level and by circulating combustion pollutants. Every year, when there is a severe cold spell and some homeowners' heating systems fail, and they resort to the kitchen gas oven/stove to keep warm, a certain number die from lack of oxygen. it's a real risk.

Before making a purchase, check with your local building codes to make sure you are not in violation. Many building codes disallow ventless systems in sleeping rooms. They may also be problematic for people with asthma or other respiratory disease and for children and elderly persons.
the Consumer Reports website used to have a good statement on the merits and drawbacks of the different systems.

If you want heat, direct vent is the way to go, but they are costly. It may be possible to get a tax credit of up to $1500 for a system that qualifies if it meets certain energy efficiency standards. If you want a pretty flame and are not interested in how much heat you will get, get a vented system. They will warm the room some, but most of the heat they generate will go up the chimney.