THG many years ago did a test on onboard and PCI NICs. It would found that the Onboard NIC used extra resources which lowered the performance of the PC by a very minor amount. That was at least 6-7 years ago, if not a little longer. I believe it was at the onset of NICs being integrated.
Anyhow, what you're looking at with the gaming NIC is a more expensive and better chipset. The short answer: The gaming NIC is better. The truth though is that unless you have a top of the line Internet Connection, the NIC isn't going to matter that much.
Your bottleneck is your internet connection. If you're running 8MB Cable with a 2MB upload a gaming NIC might give you a small performance increase. If you're running 2-5MB Cable, probably not worth your time.
PCIe is the newer version of PCI essentially. If you have extra PCIe slots, use that. It'll allow faster communication along the bus I believe. I'm a bit outdated on computer hardware but PCIe is the newer, better version.
Overall, look at what you spend on gaming. If you have top of the line everything, might as well go top of the line on the NIC. I game a little and I use an onboard NIC. I don't know that I'd waste my money on a gaming NIC. I'd put the money into something more useful, maybe upgrading a video card or paying for a few months of a faster Internet connection upload speed.