The EXACT difference would be a long post.
But they got different architectures. Intel uses LGA and AMD uses pins to connect the CPU to the motherboard.
They also uses different sockets and they have different way's to mount the CPU cooler. also they have different chipsets.
you properly already knew all this.
which of them is best? well, It basically comes down to price/performance.
Intel at this point is considered by most to be the best CPU in most cases. Servers, Gaming Rigs, Workstations and most general use.
Someone here might disagree. but you can't deny that Intel have the better architectures, and they have dropped allot in price after the launch of sandy bridge.
I am an Intel fan. but i am not a fan of the fact that Intel changes sockets all the time.
That's one of the best things about AMD in my opinion. They don't change sockets too often. So i can keep the motherboard for longer.
To me AMD is more of a budget CPU at this time.
Hardwarecanucks.com agrees. they have this continuous article each second month that talks about which CPU's they recommend for different price points. AMD is usually only recommended at the very lowest prices.