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I expected to hate #1, but it surprisingly doesn't look bad. If you didn't know the common convention of logo on the front, name on the back, you wouldn't guess anything is wrong about it. It actually fits the space better than just a logo does. Logo-less looks like something is obviously missing, IMO.
Shaved emblems are intentionally done to look cleaner but for some reason to me it makes the car look like it had collision damage repaired and the person who fixed it was too cheap to spend the extra $20-30 to put the emblem back.
#1 just looks wrong.
It's almost as bad as when people stick the Porsche "turbo" emblem on all sorts of cars like this: