Compare Overlapping FFTs to a longer FFT
That depends on your application, signal and noise.
Increasing the FFT length means better frequency resolution.
It can be shown that the FFT of a zero-mean white noise is also white noise.
Now, given that observation, this is the motivation to performing multiple shorter FFTs since the noise averages and its variance decreases by a factor of the number of FFTs.
For a stationary signal, e.g. a sine wave, the FFT should not (theoretically) change over time. Thus, averaging would have no effect. So in this case, since the noise decreases, you should expect a gain in SNR by a factor of the number of FFTs.

However, one should also take into account the scalloping loss (or spectral leakage) which can reduce the SNR significantly, and choose the FFT length correctly, according to the application.

Personally I always use overlapping if possible.