What is the main advantage of having a Layer 3 switch over a router?

With a Layer 3 switch, you get the functionality of routing and switching combined and more ports for access in a single box. The design of Layer 3 switches often provides better all-around performance than routers. The only hardware that is missing are WAN (serial) ports. So that's the difference; with a router you get WAN ports, Layer 3 functionality and two or three Ethernet ports (though for some of the Cisco router models, you can buy a 16-port EtherSwitch module which will give you 16 10/100 802.3 ports).