In addition to what sfx2000 said;
What is the reason to chose one method over the other? It just comes down to how you prefer to administer your network devices. Some people like to statically set the IP address, netmask and gateway on each device. Other people (like myself) prefer to administer these settings from a single central location. It's just personal preference.
I would mention one additional thing I like about using the DHCP method; I have quite a few devices (android phones, TV's, etc.) that have stupid host names that you can't change. By using the router's manual assignment you can give them a sensible name on your LAN, like petes-phone or lounge-tv.
An advantage of statically assigning information on each device is that they are not so dependent on the router working to communicate with each other. If all the devices are connected to a simple switch you still have some sort of LAN, albeit without internet connectivity (or probably DNS).