Carbon neutral - wood from properly managed sources (which covers the vast majority fo the UK supply), releases no more carbon into the atmosphere than it would if the wood were simply left to rot. Using a stove reduces all pollutants released by the fuel as it is burned much hotter than in an open fire, this 'secondary burn' consumes much of the pollution and means you use less fuel to get the same heat. This process reduces the release of particulate carbon.
The UK produces a large quantity eco-friendly firewood, wood-pellets and other wood based fuels, meaning transport costs (both economic and environmental) are reduced.
Price per kW - for wood is less even than gas. The only issue you may find is storing your wood. Especially if you intend to use your wood burning stove as the primary source of heat for your home throughout the winter.