A router is a dedicated routing device. It is designed and built for routing and just does that; probably very well. A layer-3 switch is first and formost a switch (layer 2 device) with added features to allow it to also make routing decisions for packets based on the information in the layer 3 header. A layer 3 switch, as long as it's good enough, will be able to perform the same routing functions as a router would; however you're less likely to get some of the wider set of features you'd find on a good router and you probably won't be able to get as wide a range of WAN circuit interfaces. And conversely you'll also be hard pressed to find a router with as many RJ45 ports as you'll get on a layer-3 switch
