I am not convinced that wood is cheaper, but it is hard to compare.
The energy value varies considerably on how dry it is and the efficiency is lower than a gas boiler maybe 80% compared with 90% for a boiler.
A kg of dried wood is about 5 kwh, so a tonne is about 5000 kwh.
The price of wood seems to vary a lot. but you can get a metric tonne dried on the net for £500, which works out to be about 10p per kwh if you assume 5kwh per kg. It seems you rarely get an energy spec on any wood that is sold and often don't even get a weight, just a "big bag".
Gas is about 7p per kwh currently, but then you also need to add in the standing charge which is about 30p per day.
I don't see the running costs that much different, stoves you have the chimney clean, cleaning and firelighters, which probably add up to similar to a boiler service per year (i would say approx. £100). If the boiler starts to break down obviously the price for parts goes up. But then a boiler probably lasts 10 years without parts, not sure how long a wood burning stove is good for.
So gut feeling is that in energy terms the costs are probably comparable. If I had to speculate I would say gas is cheaper.