Which is better a sand filter or a cartridge filter?

This depends on your definition of better. The sand will remove more and finer debris than a cartridge and its cheaper. However, the cartridge is quite convenient when it is time to replace the media. There is a 3rd filter, dietomaceous earth. Basically ground sea shells so fine its like talc. Try this site for more info about filters. I used earth for 20 years and was satisfied. Discount Pool Supplies Inground Pools