Generally, an add-on NIC can sometimes provide lower latency and assist with offloading some of the processing from the CPU. They can also have more options for configuring buffers, allowing for higher throughput. It also depends on the bus type of the onboard NIC and what you plan on replacing it with. Now adays, processors are so fast it does not really matter.
Also keep in mind that if you are talking about online gaming, your NIC is faster than your Internet connection.