The best replacement for rdp is vnc.

The best alternatives to rdp are rated as following:
★★★★★  vnc
★★★★  citrix
★★★★  ica
★★★★  vpn
★★★  rdc
★★  pcoip
★  teamviewer
★  terminal services
★  logmein
★  ssh
★  vdi
★  vnc speed
★  rdp
★  nx
★  terminal server
  splashtop
  vnc linux
  realvnc
  mstsc
  spice
  ica protocol

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

Other search terms related to rdp and their ratings are:
★★★★★ nla
★★★★ dual monitors
★★★ multiple monitors
You have in mind a companion for rdp and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of rdp in all years. Click on graph for more.
rdp
vnc
citrix