Is there any advantage to running a login script from the network or from the local PC?


This is something you should consider for laptop users.

If you place a script on the local drive of the client and point the GPO to it, the script will run at logon even if the laptop it is not connected to the network.

This is because the client side extension for scripts will still fire off based upon the most recently applied GPO.

However, the script will only perform the commands it is able to perform. Oftentimes, administrators choose to perform tasks like mapping network drives and other things which are simply not possible if the network is not available. However, again, technically, the script is trying to run