Difference between Gaussian and moving average filters for peak detection and doppler shift detection?
A centered moving average filter is a finite impulse response (FIR) filter that affects the same weight to all the samples in the window. If you only care about time domain properties, and do not care about its relatively poor performance in the spectral domain, for a signal $s$ that is quite stationary across the window, you can use it. It has extremely fast running implementation, and can be used easily for very short signals. In the spectral domain, suppose that you have the same signal amplitude at three frequencies $f_1 &lt; f_2 &lt;f_3$: $|S(f_1)| = |S(f_2)|=|S(f_3)|$. The amplitude spectrum of this filter is nondecreasing in general. So you you may end up with a filtered signal $s'$ for which $|S'(f_2)| = 0 &lt; |S'(f_1)| &lt; |S'(f_3)|$. In other words, the frequency behavior is not completely natural.

Looking at your signal in time domain, quite long and with a non stationary behavior, a Gaussian filter could be a wiser choice, if you have only these two options, and if online filtering or back feedback are not an issue. It is an infinite impulse response filter. It provides a nice tradeoff between the time and the frequency domain (in which its response is decreasing). And allow some fast recursive implementations too. You can even emulate an approximation of a Gaussian filter by combining several moving average ones of different lengths.

So I would go for the Gaussian, if your only goal is to smooth the signal.  But I believe that for more involved processing, other filters could be more appropriate. Beware of the singularity at the right end, though.