35mm vs 18-55mm at f8

I have the XE-1 with 18-55mm zoom.  I shoot mostly at f8 or f11 when I am at 55mm.  The question is would the 35mm be any sharper or pickup more detail than the zoom at f8.

I have been impressed with the zoom but wondering if I still get more out of the camera with the 35mm.  Again the question is at small apertures like f8 or f5.6

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Hank K
Nikon D800E, Fuji XE-1, RX100, Samsung NX20 (former 5DM2, GH2 Kit, and Fujifilm X100 shooter)