We love crows! I live in America, where there are three main breeds of crow, including American Crows, Fish Crows, and Northwestern Crows. They're a bit different from the Common ravens, and other ravens, found in some other parts of the world. Although there are many varieties of each, their diets are fairly similar, so to make it easy for me, I'll call them all crows from here on!
Crows are omnivores, and variety is important for their health. Their staple diet, however, is meat in many forms. Since other answers and comments have thoroughly covered that, I'll add a few other things that may work for you.
Seeds and nuts: In my experience, like yours, crows don't really like bird seed, especially the small seeds we feed the songbirds. They will eat larger seeds, though, like sunflower, (which are plentiful in my yard as that's what we feed our birds year-round) and pumpkin. Crows love nuts! We feed whole, unsalted peanuts in the shell. They take one, crack it on a nearby rock, and pick out the nuts. If we try to make it easier by putting out individual nuts, they will eat them, but if we feed both, they always choose the whole. The same is true of walnuts and almonds, so there must be a desire to work for their food, which probably stems from the same instinct as pulling apart road kill.
Berries and fruit: For much of the year, crows easily find berries and fruit on their own. They'll eat almost any wild food growing on trees in the woods, or on bushes or vines around your yard. Even things that are poisonous to people are fine food for crows. Some examples are poison oak, sumac, dogwood, and pokeberry. If you've invited crows into your yard, make sure to provide fruit year-round. Grapes, cherries, apples, cranberries, blueberries and figs are all good choices. Our crows won't eat anything in the citrus family, but your birds might.
Grains: Our crows love dehydrated corn. We sprinkle loose kernels from a bag around the yard, and they're gone in a flash! The same corn is available on the cob. These are multi-purpose. Many of our larger birds like them, and they're a huge favorite of other backyard visitors, especially squirrels and chipmunks. I've read that crows like other grains like barley and wheat, but I haven't tried those.
Miscellaneous: Our crows like whole hard-boiled eggs. We take the shells off, but it's probably not necessary. Crows also eat a variety of things that wash up on the beach. I wonder what the fish-equivalent name is to road kill. Maybe ocean kill?! You could try putting out dishes of fish carcass and leftover raw shellfish, but I haven't done it.
Backyard: Lots of living things in the yard appeal to crows, including insects, worms, spiders and small animals like frogs. Contrary to what some people say, crows can benefit the yard, as they eat the types of grubs and insects that endanger plants and food crops. They do eat some rodents, small birds, and nest eggs, but if we keep the crows well-fed, our other creatures are safer than we think.
As @michael mentioned, crows are very intelligent, and ravens even moreso. They're also quite sociable, and are content to let you sit nearby while they wander around the yard. A friend of mine in Florida has a crow that will take a nut or hunk of meat right out of her hand. Establishing a relationship like that takes time, but is well worth it!
As for being noisy while they eat, I haven't found that to be true. They may squawk when they're hungry, but they seem to make more noise in the trees than on the lawn, or at the feeding areas in our yard. I happen to love the sound, but I love all animal sounds, so I might not be the right one to give you an opinion! Ravens seem to have a wider variety of calls than crows, some being less ear-piercing and more tolerable.
The diet we use was chosen from a number of sources, and customized by trial and error. The sources include, but are not limited to:
Cornell Lab of Ornithology
How to Attract Crows to Your Backyard
The Language of Crows
Audubon Bird Guide
I hope things that have worked for us will help you. Please let us know!