If it ain't broke, don't fix it!
There is nothing wrong with using either one. If you have a good connection now, chaining to the on board will not improve performance, or security. You have 3 options at this point:
1. Leave it be and feel comfortable all is fine,
2. Boot into the BIOS Setup Menu and disable the on-board (but I can't think of a good reason to do that),
3. Connect your computer to a second network through the on-board network connect. This option, in a slightly different configuration is becoming more common. Some folks connect to the Internet through one connection, then connect to the other computers on their local network (often at 1Gbit speeds, instead of 10/100) Network card in a PCI expansion slot. Some motherboards are now coming with two 10/100/1000Mbit Ethernet connections. 