"AMD64" is x86 (32-bit) compatible, while the intel 64bit chip is not backward compatible with our current 32-bit code.
That means all software has to be recompiled for it.
If you're using open source, that has very few problems.
If you can force your software providers to do it, or successfully beg them for it, then you're ok, it's just the hassle of getting it done.
Otherwise, such as the software provider in question being defunct, you're screwed.
Consumers won't do that dance, and intel knows it; therefore they do not market it to consumers.
Even in a 32-bit os, however, applications can use some 64-bit features if compiled to do so. There's also the
NX-bit which is included only on the 64-bit versions of amd cpus.
The biggest thing in the move to 64-bit, however, is that the memory barrier at 4Gb gets broken. A 32-bit CPU cannot address memory beyond 4Gb, and therefore cannot use it. It does need an OS that can handle it too, though.
I have only used 32-bit windows, but my other box which also has a amd64 runs linux, where everything is compiled for the 64-bit cpu.
To the average user the use of 64-bit cpu/os should have no immediate impact.