Natural tend to be more expensive as they are limited. Another thing that can effect a crystal’s value is the size. Large natural ones are very rare and so considered very precious. Large synthetic ones can also fetch a very high price but are much more common.
Crystals can be grown to order. When they are being made the size, colour and shape can be controlled. With natural crystals you have no control over these things, the only thing you have control of is how it is cut.
Some people like the unique nature of natural crystals, no 2 will have exactly the same colour even if they are cut the same way.
Industry actually uses large quantities of crystals: drills, saws, ceramics, cements, and clocks amongst many other things. Industrial grade crystals are used for these rather than the more expensive gemstone grade. In industry they are wanted for their physical properties not how nice they look.
Personally I like the idea of man made crystals; mining can be very dangerous work, and I worry about the environmental and ecological impact of mining as an industry. I know that mining can bring a lot of wealth to a country but it can also cause a lot of trouble.
Anyway I find the whole crystal growing area really fascinating and I’d like to support it.