The short version
Wood burning: burns wood only. Simpler design, usually slightly cheaper, cleanest flame.
Multi-fuel: burns wood, smokeless fuel or peat briquettes. Has a grate and ash pan. More versatile if you can't always get seasoned wood.
Fuel availability
If you have a good supply of seasoned hardwood, or space to store and season your own, a wood burner is usually all you need. Wood is also the cleanest-burning fuel with CO2 emissions of around 0.008 kg per kWh (industry figure), compared to 0.198 for gas and 0.517 for electricity.
If wood supply is uncertain and you want the option of burning smokeless briquettes, a multi-fuel stove gives you that flexibility.
Cost
At the same output and brand, multi-fuel stoves are typically a little more expensive than wood burners because of the extra grate and ash pan mechanism. The gap is often small.
Maintenance
Multi-fuel stoves have slightly more moving parts (the riddling grate), but both need annual servicing and flue sweeping regardless.
Smoke control areas
In a smoke control area (most of central Edinburgh is one), you must use a DEFRA-exempt stove. Both wood burners and multi-fuel stoves can be DEFRA-exempt, it depends on the specific model, not the type. Every new stove we supply for a smoke control area is DEFRA-exempt.
Our honest take
For most Fife and Edinburgh homes we install in, the decision comes down to fuel supply. Reliable wood source? Wood burner. Want the flexibility? Multi-fuel. We'll talk it through on survey.