The alternative soilless composts were until recently based on peat, a high-nutrient organic matter found in peatland bogs. But the use of peat in gardening led to a dramatic decline of the natural wildlife habitats found in peat bogs, and ethical concerns have made it less desirable.
You can now buy reduced-peat and peat-free compost mixes. When these originally appeared, many were poor quality and that has put some gardeners off. But modern peat-free composts are much better. They are based on compost bark, coir or green manure and waste materials from parks.
Most compost types used to contain peat so look for peat-free labels. If it doesn’t say peat-free, it will contain some level of peat. If you want the best of both worlds, you can always create a half and half mix of soil-based and peat-free.