Sorry about that naming confusion. As the description says:

fft-x8664-avx.s: FFT core implementation for x86-64 AVX

fft-x8664-avx-aux.c: Auxiliary FFT functions for x86-64 AVX

fft-model-of-x8664-avx.c: C code illustrating how the x86-64 AVX code works

I understood what the programs are.

I am complaining that you don't have a C program using the AVX instructions (in C).

All the AVX functions are directly accessible from C (see: intrinsics). For a valid comparison, I would expect a C program using AVX instructions against an assembly program using AVX.

Your comparison has C-without-AVX against ASM-with-AVX. Of course, it's faster with AVX ;)