I think a lot of the early flies that became commercially available or were popularised by names are actually quite poorly designed. Usually poorly designed by people who don't/didn't really fish for carp, but tied something up and managed a fish or 2 then got the fly in a magazine or catalogue and people caught some fish so they became known as good carp flies. An example would be Egan's head stand, yes it catches fish, but that doesn't mean it's a good fly. ALl flies will catch something if enough people use them. There are exceptions to this like Jay Zimmerman's backstabber, it's as close to perfect as they get- because he actually fishes for carp and worked out what he needed. John Montanna's hybrid is another perfect fly.
As with all flies, the first consideration should be the hook. Most trout hooks are out if you're going to be encountering double figure fish and you're going to put the stick to them. Curved or scud hooks are out, most aren't srtong enough and the fish fall off them much more than standard straight or short-shank hooks. If your weird and think that curved shape matters, use a short carp bait hook and tie round the bend et voila; stronger, better hook hold, better head stand orientation. It's just better! The difficult thing is dry flies as you need them to float without the hooks being too light, I've mentioned in other FPs the Kamasan B175 is my hook of choice for this.
A LOT of the commercially available ties you'll see are tied on trout hooks.
Size matters, it's very watershed dependent. But for the most part carp will choose an inch or inch and half prey item over a 3 inch item. A lot of the early flies were big, because of the great lakes fisheries, but these are outliers. We have some here and I've often caught carp will bass fishing with flies up to 7inches. Carp eat baitfish, carp eat crayfish, but they like the little ones best. They're unlike trout, and rarely key in to a specific food item, so giving them an easy proposition is a much higher percentage option. It also takes less weight to sink a smaller fly making soft presentations easier.
Vice time also matters. This is where you can really see the trout guys' carp flies. They'll be full of little additions, so called triggers and unnecessary steps. Carp flies should be made of soft, mobile materials and be simple. All the little additions to represent X, Y & Z can be left out, the carp aren't looking for them. Look at the backstaber, the hybrid, Ryan mock's carp maul 2 or 3 materials is plenty. Any additions should add something that the carp will actually respond to, so things like rubber legs for vibration, bulk in the front to push water or high contrast colour spots to help the fish find the fly.
It's not rocket science really. Things seem to be improving as quality flies start to overtake the incumbents, but if you ask for recommendations in a shop or online try to find out if the people actually fish for carp and know what they're about.