The benefit of a large Stokes shift is that the excitation and emission wavelengths of the spectroflurometer can be set to the excitation and emission peak wavelengths of the fluorescent compound without having to worry about crossover of the excitation light into the detector. In that sense, a large Stokes shift is beneficial for measurement sensitivity.
fluorescence signal depends on the QY(quantum yield) and concentration of the compound, large Stockes shift is better for detection without interference.
Higher and lower stokes shift does not impact the intensity of the fluorescence signal. The one benefit of higher stokes shift is to get rid of self-quenching via self-absorption. The less overlap region between absorption and fluorescence is better for detecting fluorescence, especially in the case of weak emitted compounds. The quantum yield and molar extinction coefficient decide the fluorescent signal intensity.
Large stokes shift is considerable interest due to minimizing self-quenching. It is closely related to tautomerism or proton transfer. Fluorescence signal intensity depends on various factors such as solvent polarity, pH and concentration of fluorophores. QY determination either you can used absolute or relative methods for comparing lower or higher fluorescence properties. Lifetime analysis is also need to understanding radiative or non-radiative rate constant