Q: Should I keep the default stop action for virtual machines (VMs) on Hyper-V as Save or should I change it?

A: For a new Hyper-V VM, the default automatic stop action is to the Save the virtual machine state, which saves the contents of memory (and device state) to a file. This can be quite time consuming.

Typically, it's actually faster to select the Shut down the guest operating system option that's available as part of the VM properties. It performs a clean shutdown of the guest OS.

The only reason the default is the "save the state" is that saving the state doesn't  require the Hyper-V Integration Services running in the guest OS, while performing a shutdown needs the Integration Services to instruct the guest OS to shutdown.

If you have the Integration Services installed in the guest OS,  then I recommend changing the default automatic stop action to shutdown instead of save.