DE filters are more effective but a hassle
DE filters give you sparkly water, but you pay for it in labor. Cartridge filters are easier but not quite as fine.
The difference is how they trap dirt. DE (diatomaceous earth) filters coat a set of grids with a fine powder made from crushed fossilized algae. That powder catches particles down to 2-5 microns. You get crystal clear water, but you have to backwash the system and add fresh DE every time. And you have to figure out how to dispose of the used DE (don’t flush it, and check local rules for disposal).
Cartridge filters use a pleated fabric element that catches stuff down to about 10-15 microns. Still plenty clean for most pools. You just pull the cartridge out, hose it off, and replace it every year or two. No backwashing, no messy powder. Way less work.
So which one is better? Depends on how much you hate cleaning. If you want the absolute clearest water and don’t mind a little extra maintenance, go DE. If you want to spend less time messing with the filter, get a cartridge and don’t look back.
Don’t overthink it. One is a hobby, the other is an appliance.