Microsoft RDP leverages a few benefits over Chrome RDP. Microsoft's RDP protocol is better integrated with Windows as such it can work better with lower bandwith. Unlike most remote access protocols, it can pass information regarding specific windows and whether or not they've been updated which results in reduced bandwith. LogMeIn/VNC etc simply pass the full screen. Microsoft's RDP can also adapt to your resolution, sound, and access your local printers. Printing is a big one where Chrome RDP still needs some work.
In summary, for the mobile user, either one will suffice. Chrome RDP/LogMeIn/TeamViewer/etc. will do the trick on the go. However, if you are looking to replicate your workstation (e.g. printers, monitors, etc.) at home or some other fixed location (e.g. a second office or multiple offices). Microsoft's RDP is the better choice.
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