You could almost sum this up as: If you like vacuuming gravel they’re great. if you’d rather use a filter system with less overall maintenance, then they’re horrible, because they make a ton of extra work for you compared to say, sponge filters, or hang on backs, for example, which will do a better job of keeping dirt out of your system, as they don’t pull the dirt into your gravel.
Fish stores love them because they can drive a ton of tanks with huge air pumps, all at once, and they can just vacuum gravel while they do water changes. Plus, there’s little if any decor in most fish store tanks – so vacuuming around plants, rocks, or decor is usually no big deal. However – even for this purpose – I’d still argue – sponge filters are better. You can simply pull them out, squeeze them in a bucket of tank water, and put them back, done. It doesn’t pull dirt into your gravel, making gravel vacuuming not just an occasional routine chore but an absolute necessity to prevent it from becoming a literal cesspool under the gravel plates. You wouldn’t need to vacuum nearly as much with sponges.
And if you’ve ever been to a fish store that has a bunch of tanks driven off under gravel filters, and can look under the tanks from the glass on the bottom, especially if they’re on an open frame, go take the opportunity to do so, and look at the built up gunk under there, which you can basically never clean, as it’s stuck under the gravel plates.
Sponges are better from a purely technical and maintenance standpoint, if you need an air-driven filter, but they are unsightly, ugly, and take up tank space, compared to gravel filters, from a visual/aesthetic standpoint.
A hang on back, is ultimately a nicer solution for a basic small display tank, as it’s easy to clean, the filter media is readily accessible (unlike say, a canister, which is totally another option, but they are more difficult to clean, and in saltwater, often become detritus traps), and it’s not nearly as invasive in your tank as a sponge. They also provide great mechanical filtration, and move a lot of flow, as well as provide a lot of surface oxygenation, making it less necessary to need an air-pump at all, and for smaller tanks, they’re my go-to these days, often with just a wave pump or air-stone added for redundancy (never know if one day there’s a power outage and a filter doesn’t prime, etc…)
For larger tanks, and most of us in the saltwater world, it’s hard not to want to suggest a sump as the go-to filtration method. Keeping your dirty filters separated from your display tank is never a bad thing.