People mainly choose quilts rather then sleeping bags, because they want to save the weight and carrying full weight of sleeping bag is unnecessary weight carried for them.
Compressed down or synthetic insulation under your body on the bottom of a sleeping bag provide no insulation and therefore can not store warmth. If you have good sleeping pad for insulation to the floor then compressed bottom insulation is useless and not needed. This will save the weight, because no insulation wasted under you.
Quilts are also lighter then sleeping bags because of missing zipper and hood.
Quilts are obviously cheaper because of less down, less fabric, no zipper, etc
FREEDOM OF MOVEMENT
People love quilts for the freedom of movement. Many people who sleep on sides or on stomach have found quilts to be better solutions compared to bags. You can move as much as you like under it. If you dislike sleeping in mummy bags, beacuse it is too tight and uncomfortable for you, then sleeping in quilt will be much better for you.
FREEDOM OF CHOICE IN CLOTHING
You can choose and wear whatever you want under it to suit temperature. You can wear whatever you want on your head for warmth and not get smothered in the hood. You can use your warm clothing to extend the comfort temperature of a quilt then it's also nicer to get out of because you don't lose all your insulation when you crawl out, so you don't freeze half naked in the tent while you try to get dressed.
Quilts are more efficient and have a high warmth to weight ratio. Why? no insulation wasted under you, no fabric weight directly under you, no hood weight, no zipper weight.
Simply shape and no zipper to fail (weight saved). Because quilts are simpler you can make your own more easily than a sleeping bag.
Depending on style many quilts can be laid flat or formed and sealed around you. Adding features: wings, loops, straps on the sides, velcro strips or elastics to form a footbox, draw cords or drafts stoppers help you to adapt it to your actual needs and conditions. Some quilt have some type of footbox (sewn or can be formed) to keep your feet warm if it gets cooler.
Use it as top quilt, underquilt in hammock or as a coat. Possibility to use it inside of a classic sleeping bag in order to improve insulation. For home use: expect serious heating savings!