Spectral Content of two waveforms
Your intuition is correct. The reason is that the rectangular pulse train has  discontinuities, whereas the rectified sine is continuous (but its derivative has discontinuities). The consequence of this is that the Fourier coefficients of the rectangular pulse train decay as $1/n$, whereas the coefficients of the rectified sine decay as $1/n^2$ (where $n$ is the index of the Fourier coefficients).