changings gas logs fireplace to insert
If you are talking about a gas log set in a masonry fireplace then you need to understand that these log sets are not really expected to heat the room aside from a bit of passive radiant.  In fact, the room could experience a net loss in heat.  The flame from the gas log will heat the chimney flue causing a good draft and will suck the heat right out of the room. These things were designed for ambiance without the mess of chopping wood. They are quick and clean.  That is it. 

Ben Franklin designed the Franklin stove to beat the disaster of a heat source of the old masonry fireplace.  

The modern natural gas steel fireplace insert is a big step forward.  It will actually make heat.  They have been engineered to extract heat from the fire and get it into the room.  With the right size they can easily heat a typical room of a 1000-Sq feet.
It is however not necessarily the most beautiful thing that ever walked the down the isle. Some have glass fronts to give you a view of the fire.    

Cost effectiveness? Something you have to decide.