It has nothing to do with efficiency. The native and cross-compiler will both generate the same machine code. You will however gain some benefits by running a native 64-bit compiler process on a 64-bit workstation (larger registers, larger memory space, etc…).
The native compiler will only run on an 64-bit copy of Windows, so if your workstation is 32-bit this compiler won’t even run.
The cross-compiler is meant to run on x86 machines even though it will run on a 64-bit copy of Windows via WoW; however, there is no reason to do this.
The page you link says it quite well:
x64 on x86 (x64 cross-compiler)
Allows
you to create output files for x64.
This version of cl.exe runs as a
32-bit process, native on an x86
machine and under WOW64 on a 64-bit
Widows operating system.x64 on x64
Allows you to create output
files for x64. This version of cl.exe
runs as a native process on an x64
machine.Thanks to Brian R. Bondy for the quote formatting