It’s important to avoid using multipurpose compost that contains peat, because of the large amount of carbon dioxide that’s released into the atmosphere when peat bogs are drained in order to extract the peat.
Peat bogs are also important for biodiversity, as they’re unique habitats that support a range of rare plants and other wildlife.
Until recently, peat-free composts tended to be more expensive, and sometimes less reliable; but this is changing as manufacturers adjust their formulations and improve their supply chains. The one real difference for ordinary gardeners is that many peat-free composts hold more water, for longer, than the old peat-containing multipurpose composts, so we have to be careful not to over-water seeds and seedlings (the top may look dry, while the compost underneath is still wet enough). This can be very useful in drought! – but it’s something to be aware of when starting seeds off.
There’s likely to be far less difference in price between peat-free and the older peat-based multipurpose composts, as an increasing number of countries ration licences for peat extraction, or ban it completely. Ireland was our main supplier (the UK has already exhausted most of its peat bogs), but they’ve banned peat extraction now.