When should I start outsourced manufacturing from a PO vs. WO? Both seem to be have the same features? Is it just a matter of who initiates it: purchasing vs. manufacturing team? Does NS WMS and manufacturing mobile support outsourced PO and WO?

If you create the work orders first you have an opportunity to aggregate PO's to a vendor. So if you create 4x Outsourced work orders for different items that all have the same vendor they will become available in the Setup > Manufacturing > Outsourced Manufacturing tool to create the po. Or the PO would generate automatically at 2am. I'm not sure what purpose NS WMS or MFG Mobile would have when it comes to outsourced manufacturing? The WMS would pick up the transfer order for components out to the vendor location and the finished assembly once it was received (probably required to do the reciept / build from the UI) and the MFG Mobile would be able to consume the assembly into another assembly but probably won't be able to be built using it since it is not a trad build.

Both work, but as Bryan said, it is optimize in one way using "outsource manufacturing" in Manufacturing tab under Setup.