The list here https://www.toonboom.com/products/harmony/pricing gives you a basic overview.
Filters: Blur-Radial, Colour-Scale, Glow, Shadow, and Transparency. Advanced only offers two more: blur-gaussian and colour-override. Compared to Premium: 38 filters. http://docs.toonboom.com/help/harmony-14/premium/reference/node/filter/filter-node.html
Drawing: no bitmap painting tools.
No wav export. No 3d objects support. No particle systems (so no easy rain or snow animation).
Render output is limited to 2k.
To be honest, Essentials is a very cut-down version - good for beginners, but I’d say you are better off looking at alternatives (OpenToonz, Toonz Premium, Moho) if you cannot afford either Advanced or (better) Premium. Even OpenToonz (open source and free) offers scanning, vector drawing, nodes, curves/graph editor, a nodal compositor with a wide range of filters (more than Harmony Premium includes), bitmap drawing, unlimited render output size, particle systems, etc. etc…
Perhaps I am overly harsh, but in my opinion Essentials should not be offered anymore in lieu of what the competition now offers. I don’t really see the point of Essentials anymore.
You can compare the editions in detail here:
Open the REFERENCE section, and compare the NODES.