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The resolution of spectral analysis depends mostly on the length of the time interval in which the signal is collected. Roughly the delta f (the frequency resolution interval, or the difference in frequency that you can 'resolve' or separate) is 1/T0, where T0 is the time length of the signal collected. Clearly T0=N*T, where N is the number of samples and T the sampling interval (1/(sampling frequency)). Apart from this there are some (minor) differences of frequency resolution that depends on the technique used for spectral estimation, for instance, autoregressive (AR) - spectral estimation is marginally better than Fourier analysis, especially for short time windows T0). Do read the excellent paper by Kay and Marple on spectrum analysis (Proc. IEEE, 1981): http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1456452

Please see this paper and its references:

http://www2.leicester.ac.uk/departments/engineering/people/academic-staff/fernando-schlindwein/publications/Autoregressive%20spectral%20analysis%20as%20an%20alternative.pdf