1. Open fires are very inefficient and most of the heat goes up the chimney. Open fires are typically only around 20% efficient.
2. A wood-burning stove re-circulates combustion particles and is designed to burn at a much higher temperature. This means gases present in the smoke are fully burned which results in a thermal efficiency of around 80%.  In other words you can get around 4 times as much heat from a log burnt on a modern wood stove than from an open fire. 
3. The heat from an open fire heats a relatively small area whereas the heat from a wood stove radiates over a much larger area.  
4. Wood burning stoves are less smoky than an ordinary open fire and produce less ash and mess. 
5. Wood burners are safer because the fire is enclosed so you don't get the danger of stray sparks or hot coals on the carpet.

Open fires produce 80% more particulate matter than the new Ecodesign Ready stoves.  This particular matter is causing great concern about air quality in London and other major cities.  It is understood that diesel cars are the major producers of particulate matter but it is believed that wood burning on open fires in London contributes 10% of particulate matter.  Replacing your open fire with an Ecodesign Ready stove could reduce your particulate matter production by 80%