I currently have a DE filter. My son, (who lives across the street) has cartridge. My best friend and neighbor has sand. Both my son and I have SWG, but my friend does not. If I were to replace my filter now, I would go with a cartridge.
Here is my reasoning.
I am not so concerned about how fine it filters, or how difficult it would be to clear a green pool. All three types filter fine enough to produce crystal clear water, and in the 15 years I’ve had this pool, I have only seen a tiny tinge of green once (when my SWG failed). I would not want a sand filter, because the amount of water discharged during the frequently required backflushing. That lowers my salt level, my CYA, my borate level and means I would constantly be replacing chemicals, and rebalancing the water. I currently use hairnets in my skimmers and use a robot to clean the pool, in order to minimize the debris going in to my filter, (and thus maximize the time between backflushing). To avoid the constant rise in CH, (due to the hard Tucson water, and very high evaporation rate) I have my auto fill connected to my water softener. As a result, I backflush about twice a season and haven’t had to drain the pool in about 5 years. I would prefer a cartridge filter and NO backflushing.
My friend‘s sand filter works for him, because his is not a SWG pool. The frequent backflushing actually works in his favor, lowering his constantly rising CH and CYA levels.