The best replacement for sony rx100 is canon s120.

The best alternatives to sony rx100 are rated as following:
★★★★★  canon s120
★★★★★  panasonic lx7
★★★★  canon g1x
★★★★  canon s110
★★★★  canon s100
★★★  canon g16
★★★  canon g15
★★★  fuji x100s
★★  nex 3n
★★  ricoh gr
★  fuji x20
★  rx1
★  nikon v1
★  lumix lx7
★  nikon d3200
★  sony rx100 ii
  nikon j1
  fuji x10
  lx7
  canon gx1

Your alternative for sony rx100 is not listed? Suggest!
Speaking about sony rx100, one probably shouldn't forget about canon s100.

Other search terms related to sony rx100 and their ratings are:
★★★★★ canon s100
★★★ canon g1x
★★ lumix lx7
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sony rx100
canon s120
panasonic lx7