The differences are more in the base plate design than the cap. The SC base fully supports the blade even to a point slightly past the end of the cap as the pics from rabidus show if you look closely. The LC base has no where near the support on the base.
SC on the left, LC on the right.
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As you can see, the base plate support on the LC base ends well short of where the blade edge would be. That contributes a great deal to the smoothness mentioned when shaving ATG. The LC I had I gave away as I couldnt get a BBS shave over the two trouble areas I have on my neck, even with a shim. With the SC, it takes the stubble off like it never should have been there in the first place, effortlessly. As it turns out, my nephew that I gave it to also has ATG issues with it and has moved on to a Single Ring that has virtually the same base plate support, without the gap of the SC base.
For a simple eye opening test, load a blade in both your LC and your SC and try to deflect the blade edge downwards towards the comb with a paper clip or something similar. You'll see how much, and how easily, the blade edge will deflect on the LC. Whereas the blade in the SC will feel as though its a part of the razor head itself its so solid. That flex acts like a spring when shaving ATG, and for me, even when shimmed, skipped over the stubble on my trouble areas.
The pictures below are of the caps. SC on the left, LC on the right. Notice the corner tabs and how the tabs on the SC cap lock into the recesses in the base plate vs the LC tabs that only serve to help align the blade.
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Both razors side by side.
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Other than a Wolfman WR1 razor, I'm not sure theres a DE razor design that holds the blade as securely as the SC does with the proper SC cap.
I just read the entire thread (outstanding info) and had to go check and make sure my NEW SC had the correct top cap...it does!