The best replacement for psd is tiff.

The best alternatives to psd are rated as following:
★★★★★  tiff
★★★  jpeg
★★  eps
★★  psb
★★  png
★★  ai
★  fft
★  dng
★  cummins
★  tif
  asd
  pisq
  uciw
  eps files
  v10

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Other search terms related to psd and their ratings are:
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