From the documentation it appears that the Lite FFT is something that meets "requirements of 3GPP LTE standard" which, based on a quick google search, is a mobile communications standard (not sure what that even is) defined by a group of organizations. This appears to affect the transform's "length" which I'm also not sure of the meaning of a transform's length (time, # of bits, # of summing iterations etc).
The FFT appears to just be a regular algorithm for a FFT.
I'm just trying to make a PID controller and I'm not sure which FFT I should use. I just need the fastest/most accurate FFT and possible compatibility with MATLAB (which I see the FFT one does have).