Which one is better for frequency detection? In what circumstances? Advantages and disadvantages of both? Which would be better for a Voice Activation Detection algorithm? Which would be better for an instrument tuner? How would one detect pitch user an HHT transform? Is it faster than FFT? How would one implement HHT?
Fourier algorithm is actually a global transform that can not reflect the damping and local specialty. Unfortunately, these features are fundamental and important for characterize a nonstationary signal. on the other hand in the Fourier algorithm the estimation of frequencies are sensitive to noise. so HHT is better in your case if you are going to deal with noisy signals.