Public is the most secure, but you really don't need to use it at home, use hardware, like wifi router, firewall to keep secure.
What are you not sure about ? Public network setting - This location is designed to keep your computer from being visible to other computers around you and to help protect your computer from any malicious software from the Internet. HomeGroup is not available on public networks, and network discovery is turned off. You should also choose this option if you're connected directly to the Internet without using a router, or if you have a mobile broadband connection. Remember even if you don't have a router but use a cable modem, the modem can have a firewall setting also.
"Cuteees Quest To Bend Windows 10 Home" ... should be in movie theaters near you soon, Cortana will notice you .
If you have a router, then you must also have a modem, so now you have three firewalls in theory if they are configured. Private is less secure, and you can see how you are visible, but like I said, usually home won't matter unless you live in an apt and have a 100 people around you, and you're using wifi, and if you are and use home, people will see your network. But if it's secure, they would need to hack into your network.
If you don't need to network to all the PC's in your house or any hardware like printers through wifi, then stay on the public network setting as it is the safest, and you have no reason for networking.
On every my PC/laptop I always set public network even if I have already a router at home. I set this because if I moved with my PC to friends or other for assistance, I really don't know how are their network/internet
Then if you don't use any wifi, or you're not networked to any PC's that have wifi, then the home setting is secure. You don't need to use public. But you asked which is more secure, in theory the public one is.
You can change the firewall to block all traffic. You could then make specific rules for each program. It's really annoying, tho. I wouldn't recommend it.