AMD64 has no byte swapping load and store opcodes. If you refer to MOVBE, it was first introduced on Intel's Atoms, and then on subsequent Intel's processor. Later it was also implemented on AMD processors.
So, MOVBE isn't part of the standard AMD64 ISA, but only some processors have it (there's a CPU flag to check for its presence).
MOVBE is definitely MUCH better than BSWAP, because it allows to load and store BE data using any x86/x64 addressing modes, which is a vast improvement over the BSWAP. And performances gained much more benefits compared to the latter.