The best replacement for brink is bulletstorm.

The best alternatives to brink are rated as following:
★★★★★  bulletstorm
★★★★★  crysis 2
★★★★★  rage
★★★★  homefront
★★★  adt
★★  verge
★★  killzone 3
  rndq
  dianavanden brink
  on the blink
  socom 4
  brim
  on the brink
  at the brink

Your alternative for brink is not listed? Suggest!
Speaking about brink, one probably shouldn't forget about ffdp.

Other search terms related to brink and their ratings are:
★★★★★ ffdp
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Google Trends

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brink
bulletstorm
crysis 2