If my aging brain remembers correctly, AMD was the first to push the x86_64 in the AMD64 architecture when all Intel had for 64 bit chips was IA-64; and they were also the first to bring AMDV/VT-x to midrange desktop chips (for a while it was only available on Xeons from Intel). They also had better performance per watt than the Intel Chips at the time. It was a good time for AMD but they fell behind when Intel came out with Core2 (based on Pentium M). Since Core2 (and subsequently the iN series) they've been playing catch up, but not too long ago they were the leaders.
I think the AMD64 architecture was probably the most significant in those days because it meant that you could run more than 4GB of RAM without PAE overhead.