The best replacement for axe fx is kemper.

The best alternatives to axe fx are rated as following:
★★★★★  kemper
★★★★★  eleven rack
★★★★★  tube amp
★★★  guitar rig
★★★  line 6
★★  pod hd
★★  pod
★★  eleven
★★  amplitube 3
★★  eventide
★★  axe fx ultra
★  pod hd500
★  hd500
★  pedals
★  strymon
★  bias
★  amplitube
  line 6 hd500
  guitar rig 4
  rocktron prophesy
  triaxis

Your alternative for axe fx is not listed? Suggest!
Speaking about axe fx, one probably shouldn't forget about power amp.

Other search terms related to axe fx and their ratings are:
★★★★★ power amp
★★★ ground control pro
★ fcb1010
★ 4 cable method
★ carvin ts100
★ qsc
You have in mind a companion for axe fx and it is not yet here? Propose!



Google Trends

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axe fx
kemper
eleven rack