I haven't used the SS, DX, or clones. I have handled a Kai Captain, but never shaved with one. I can do a features vs. each other comparison, but cannot speak for the shave itself.
Let's take a look at the razors in question. I took the picture of the DX off the internet, but we'll trust it's a accurate representation. The Essence pictures I took myself and tried for as close as I could get to the same angle. Both razors were photographed without a blade installed.
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@Snuff would have to confirm, but visually, if you take one of the bag clip halves off a Feather DX, what you would be left with is a blade slightly skinnier than both halves of the Essence blade holder.
The DX uses a spring and clip arrangement, plus a slot and peg setup to lock the blade in place.
The Essence has a relief cutout for the blade to rest in, and two pegs to rest the top of the blade against, and the tension of the two halves, held together by powerful neodium magnets, is what holds the blade in place, and does so very securely.
Side note here. The IBC shavette also uses magnets, but in a different way. The magnets hold the blade while the blade holder is tightened via a thumb screw. I believe that IBC patented that method of blade holding for a shavette. The Essence side steps their patent completely, while still using magnets.
Back to the post. The 4.2 mm (at it's widest point on the blade) Essence is narrower than the DX. This allows the Essence a greater range of blade angles than the DX.
Fit and finish between the two? We all know the DX has one of the nicest finishes in the shavette world. The Essence is on a different level. It's not an apples to apples comparison.
One was designed to shave a person quickly and smoothly in the hands of an expert. The other was designed to mimic a straight razor in look, feel, and shave.
Hope that helps a bit.