I've posted about this somewhere else on this site, but I'll go more in depth here.
As the OP states, the Shadowfell and Feywild are echoes/reflections of the Material Plane. The Feywild is closely tied to the Positive Energy Plane, and the Shadowfell is closely tied to the Negative Energy Plane. The Feywild draws its energy from an infinite font of possibility, warping the Material Plane where it touches it and founding its own plane of existence filled with the vibrant emotions and stories told by the denizens of the Material Plane since the dawn of time. The Feywild's light shines upon the Material Plane, and creates a Shadow Realm reflection of it directly on the other side of the world (on the cosmological and metaphysical scales, that is). The brightness of the Feywild's energy creates a realm completely opposite of it, filled with nothingness and void that is lacking in the Feywild.
The Feywild is created by the Material Plane, as is the Shadowfell. If there was no Material Plane, there would be no Shadowfell and no Feywild. If not for the imaginations, wishes, and emotions of those that lived on the Material Plane, the Feywild would not be filled with the embodiments of these imaginations, wishes, and emotions, and the Shadowfell would thus be nonexistent, as the dark reflection of nothing is still nothing. The vibrant Feywild evolves as the Material Plane progresses, and the Shadowfell also changes to reflect the progress that the other two realms undergo. As more people exist on the Material Plane (thus creating more wishes and emotions), the Feywild grows in size and population, and the bleakness of the Shadowfell grows.
Lesser Fey are mostly the embodiments of simple emotions and/or ideas, like bloodlust (Redcaps), disgust (Hags), mischief (Boggles and Quicklings), the beauty of darkness (Darklings), the beauty of nature (different types of Nymphs for different parts of nature; Dryads for forests, Naiads for rivers/the sea, Lampads for the Underdark, etc), paranoia (Meenlocks), frustration (Mites), careful curiosity (Pixies), revelry (Satyrs), and so on, and so on.
Greater Fey (mostly Archfey and Hag Matrons) are the embodiment of more complicated wishes and stories. The Prince of Frost is an embodiment of the tragedy of not being able to let go of someone that you love, Baba Yaga is the embodiment of the narcissistic "Mother knows best"-type parent that abuses and corrupts her "daughters", Verenestra is the embodiment of the frivolity of existence and the sinister pleasure that comes from manipulating those with less power than you. Greater Fey are stories and wishes, while Lesser Fey are simple emotions and ideas.
The Sorrowsworn and other shadow creatures of the Shadowfell are physical polar opposites of the extreme emotions of the Feywild. While there could be a Lesser Fey creature that embodies gluttony, there would be a Sorrowsworn that represented the Shadowfell's lack of food (the Hungry), there are fey that embody beauty, so there are Sorrowsworn that embody the Shadowfell's lack of beauty (the Wretched), there are fey that embody friendship, so there are Sorrowsworn that embody the loneliness of the Shadowfell (the Lonely and Lost).