Curious, as I have some people telling me different things. Does either of these affect a vpn?
That depends on the nature of VPN.
Private and Worspace networks allow connectiont to Windows services of your computer from entities on the networks. Public network disables them.
Using VPN to encrypt the connection to Internet, like it is advertised everywhere, is actually a misuse of technology. In this case there are supposed to be only 2 machines on the network - your and the exit server. Assuming you trust the exit server not to connect to you, there is no difference between setting the network as public or private.
But if there are other clients on the VPN network, and if you are using VPN as supposed to be, to connect multiple PCs from different places in one net, then the private setting allows those clients to access services on your machine.