No. The complex (and r2c) FFT algorithms are much more optimized in FFTW than the r2r plans, e.g. the former use SIMD and the latter do not. So even though a complex FFT takes about twice as much arithmetic as an R2HC plan of the same size, the former’s greater optimization makes up for it.

As explained in the FFTW manual, we generally recommend the r2c interface if what you want is a real-input DFT, especially in the multidimensional case. The r2hc algorithms are included mainly as stepping stones to other transforms, and because it is occasionally convenient to have a real-input DFT where the output is exactly the same size.

This is too bad since r2r is useful for Chebyshev transforms. I remember for certain degrees this caused ApproxFun to be much slower than Chebfun (which just translated it to an FFT).