The best replacement for intel atom is intel celeron.

The best alternatives to intel atom are rated as following:
★★★★★  intel celeron
★★  tegra 3
★  tegra 4
★  marvell armada xp
★  amd fusion
★  intel core
★  intel pentium
★  apple a7
★  amd athlon
★  amd neo
★  snapdragon 800
  raspberry pi
  arm cortex
  via
  pentium m
  nvidia tegra 3
  dual core processor
  via c7
  quad core
  intel mobile
  amd geode

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Speaking about intel atom, one probably shouldn't forget about nvidia ion.

Other search terms related to intel atom and their ratings are:
★★★★★ nvidia ion
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intel atom
intel celeron
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