The quilting layer of a mattress is part of the mattress cover itself and is the top cushioning layer of a mattress. Like other layers it can perform a dual function. One of these functions is to add thickness and softness to the comfort layer if this is needed and in this way it functions as part of the comfort layer itself. This is particularly true when there is foam in the quilting such as memory foam, latex foam, or polyurethane foam. The different foam used here would have the same advantages and disadvantages as when they are used in a comfort layer and the foam in the quilting should be considered as part of the comfort layer itself. The second function is to add certain properties to the mattress such as breathablilty, temperature regulation and fire retardancy to the mattress.
Other than foam, you will commonly find various types of natural and artificial fibers or materials in the quilting layers. Some of these can add to a subjective feeling of softness or "cush" on top of your mattress and produce part of what is called the "hand feel" of a mattress which is how it feels to the touch or with a very light weight applied. While some of these materials can feel very soft to the touch, this does not necessarily improve a mattress' ability to relieve pressure and can in some cases even reduce it over time. This is because most natural or artificial fibers will either soften and break down (most synthetic fibers) or compress (most natural fibers) over time and as this happens it will affect both feel and performance and can change the support and pressure relieving qualities of the mattress.
It is also important to recognize the difference between a material that relieves pressure by spreading weight along the entire sleeping surface of the body (like a foam) and a material that just feels soft to the touch and which may provide some cushioning effect to more localized parts of the body (like a fiber). Some fibers (such as wool) because of how they are connected to the mattress (tufting or different quilting patterns for example) or because of their own natural qualities do have some resilience and "elasticity" and can help to a greater degree with localized pressure relief however this is rarely to the same degree as foam. Most synthetic fibers or non woven materials (such as some types of down replacement or fiberbeds) can also add localized cushioning and pressure relief for a while until they soften, compress, and/or break down however they will not last as long or perform to the same degree as a high quality softer foam or even most well made natural fibers.
Wool can also act as a natural fire barrier and there are those who prefer compressed or densified wool in a quilting layer as an alternative to a different type of fire barrier such as viscose impregnated with silica or cotton with boric acid. While wool quilting may reduce pressure relief to some degree depending on the type and thickness and compression of the wool and on the firmness of the foam below it ... (more in the longer term as it compresses) ... for some this is a welcome trade-off for the breathability and temperature regulation of a natural fiber and on the ability to avoid synthetic materials in their mattress.
Some fibers, particularly the natural ones such as linen, silk, wool, and horsehair are very breathable and because of this and their ability to maintain their insulating abilities when they are moist can add significantly to the temperature and moisture regulation properties of a mattress which can significantly improve the quality of sleep. This is particularly true when they are used over comfort layer materials that tend to sleep hot such as less breathable foams like memory foam. There is also some evidence that this temperature regulating quality of natural fibers, in particular wool, can help in maintaining deeper sleep and aid in overall rest. For this reason they are often used in spite of the "tradeoff" of slightly less pressure relief. An alternative of course is to add a mattress pad with these materials which can be replaced when it compresses or wears out although.
A quilting layer can be made to be tight (firmer) or loose (softer) across the surface of your mattress while mattress toppers will always be softer. Tighter and firmer quilting layers and patterns can in some cases even act as a form of zoning which can help so some degree with alignment however it will do this at the expense of pressure relief and it is more common and effective to control this in other layers of the mattress. Quilting layers that use various techniques to help maintain loft such as tufting and tack and jump can help a fiber quilting layer to stay lofted and prevent shifting for longer than a mattress pad however it has the disadvantage of not being replaceable when it becomes compressed and starts to affect the feel and performance of the mattress.
Down is neither a fiber or a non woven and since it retains its ability to be re-lofted over long periods of time, it is a popular way of adding a feeling of softness to a mattress that doesn't interfere (at least in reasonable thicknesses) with the ability of underlying layers to relieve pressure to the same degree as other materials. Some down alternatives now available are also good in this area although it is questionable how long they will last in comparison to down. Down though is not as good at wicking away moisture or regulating temperature as natural fibers, does not maintain its loft and insulating qualities when moist, and is also more subject to dust mites than natural fibers such as wool.
Even subjective feelings of softness plays a role in the quality of sleep and a mattress that feels good to lie on will lead to sleeping better or at least falling asleep easier, even if it does not help directly with pressure relief or support. Imagine going to sleep on rough burlap for example which would not likely interfere with pressure relief but could certainly interfere with the overall feel and comfort of the mattress ... even if it was covered with sheets or through pyjamas. The human skin is particularly sensitive and our own subjective preferences play a role in everything we do so and the mattress quilting can add a little "cush" or other properties in the top of your mattress which may help you sleep better ... although it may also be worth considering adding these qualities with a mattress pad instead.
In the end ... the choices are all about the tradeoffs that best satisfy the preferences of each person.