Powershell on Linux
Is as dumb as bash on Windows. I know bash and don't know Powershell, but if I had to write scripts that would be long lived and supported for Windows machines, I'd either learn enough Powershell to get the job done or (this would be my first option) hand it to a Windows guy who already knows it. I'd only use bash on Windows if I was writing some quick and dirty scripts for my use alone.
Using bash on Windows or Powershell on Linux just leaves a future support headache as you reduce the audience of people who are able to understand/modify the scripts, and you have a special environment that needs special handling rather than being a native part of the OS like bash on Linux or Powershell on Windows.
In fact I had this dilemma years ago when I was writing scripts to extract/massage data off DMX arrays all over the world. The tools were installed on Windows boxes at some sites, and the path of least resistance was to install an SSH server on them with certificate login allowed from a single host (approved by security after countless meetings I was billing a lot for :)) and created a VM as a Linux scripting host. It used ssh to grab the data it needed from Linux & Windows hosts, and scripts were processed in Linux.