They're 2 very different companies that create processors based on x86 architecture. The posts above are correct, however in addition to that there's more.
Instruction Sets and their implementations: Most of AMD Processors and Intel Processors use similar instruction sets, but there is also some deviation from the standard norm. These is why they have so many different variations in applications outside of gaming (ie media encoding).
Architecture: Yes they both produce x86 architecture however they design them differently, ie Intel will be using 3d Transistors in Ivy Bridge, while AMD has been recently combining an extra Integer Processing Unit into a core and saying that it's dual core.
Power Wattage: Intel's offerings are usually more power efficient than AMD's.
And there's probably more differences as well.
Right now, as of Today (Oct 18 2011), Intel definitely has the lead. Intel i5-2500K is comparable in performance (across the board) to AMDs new FX-8150 and it's about $30-50 cheaper, but when Q1 2012 comes and we start to see AMD's PileDriver and Intel's Ivy Bridge that might be a different story.
On a side note, why does Antec even have it's own section?