There was a time when you have one or several computers at home, and the only way to get on the Internet is by using a browser on one of the computers. You would install parental control software on these computers to prevent kids from seeing inappropriate material, or spending too much time “surfing”.
Nowadays, a lot of families have multiple digital devices that kids can use to get on the Internet, such as smart phones, tablets, game consoles to name a few. That means you have to install and configure parental control software on each and every device in order to keep effective protection. Since each type of device has its own way of doing things (such as installation, device management etc.), that means that you have to gain at least some expertise on each device platform. Sometimes, you may not even find suitable software for the device at hand. It is a very time consuming task to say the very least. And depending on the number of devices and how much time you have at hand, it may or may not be feasible.
You may want to control things at the router. Since all Internet traffic travels through the router, all devices connected to your home wifi network are effectively protected. For example, if you successfully blocked facebook at the router, your child cannot visit facebook from your home network, no matter what device or browser they may chose to use.
One drawback for the router approach is that it does not offer the same granularity as the software approach. For example, it’s not possible to do keylogging on the router. It is not possible to enable or disable games, or take screenshots. Software is still the way to go if you need fine-grained control. After all, it doesn’t have to be an “this or that” decision. You may choose both router control and software control to supplement each other.