I understand the advantages of SC-FDMA over OFDM and I also understand the disadvantage of additional complexity (FFT block), are there another disadvantages?

Also, if $N$ has to be bigger than $M$ ($N>M$) then I don't understand why I don't lose rate as a result of padding with zeros instead of transmitting another data subcarriers.

Regarding the data loss: Even if $M<N$, there is no real loss, because the used bandwidth of your signal is only M frequency bins (ignoring any guard carriers). So, any other system can use the remaining N-M frequency bins.
• 0dB echo path or any other multipath, you essentially have the following signal model for your single-carrier: y=Hd+n, where n is noise, H is the MxM (circulant) channel matrix and $d$ is the transmitted data. It's equivalent to a MxM MIMO system. You can now do linear equalization by "dividing by H". Here, only the LMMSE equalizer can gain diversity, but only for higher SNR. The ZF-equalizer will not gain diversity. Or you can use a non-linear technique, like a sphere-decoder to get to the d-values with even better performance. VOFDM gives you more frequency diversity by wider data spreading. – Maximilian Matthé Feb 22 '17 at 21:28