What is the difference between general microprocessors, DSP and FFT chips?
In addition to the memory differences that David pointed out, DSP chips have multiple multiply/accumulate (MAC) units.  MAC is a very common signal processing operation that is the basis of filter and FFT/iFFT operations.  Some DSP chips that I used in the past had six MAC units, which allowed them to speed up the FFT operations in two ways: they could do six MAC operations at once, and the MAC operation itself would take one clock cycle while on a general purpose microprocessor each MAC would take at least two clock cycles since it would be a multiply followed by an add.