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What kind of filter you use is almost entirely a personal preference issue. There are some differences between the various filter types but they are fairly minor. For example a cartridge filter makes the most efficient use of water, since rinsing the cartridge off takes much less water than backwashing a sand or DE filter. DE filters filter down to a smaller particle size than other filters, sand is the "worst" and cartridge filters are in-between. However, most people can't detect any difference caused by that.
The main differences are in the approach to cleaning the filter. Cartridges get removed and rinsed off, sand gets backwashed, and DE gets backwashed usually and occasionally needs to be opened up and throughly cleaned.
The size of the filter make a dramatically larger difference than what kind of filter you have. Larger filters can go longer between cleanings and are slightly more efficient.