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I don't know about the same lens, but the glass is vastily different as it have more of a spread compare to the spotlight beam of the Supernova, and while it doesn't appear as bright in cities, it still lit up road better.
It also have a cut off, meaning that you can position the light a little higher without dazzling incoming road user, a problem I found with the Supernova and have to resort having it pointed slightly down than horizontally.
(I used both Edelux* and Supernova in audaxes).
*I used the old Edelux that was pretty good, but the Edelux II outshine it easily.
This image is a pretty good example showing where the light cut off just above the road like a cars;
The Supernova from memory is exactly like this, but I mount it a little lower as that position dazzle incoming cyclists in Richmond Park (I turned on my hearing aids only to realised people been shouting at me for a fortnight);
My advice would be the Edelux II, then Supernova.