What is the difference between Slow Feature Analysis (SFA) and a Moving Average?
Mathematically, SFA differs from moving average by the fact that the instant output $y_t$ can only be a function of instant input $x_t$. On the other hand, the output of moving $y_t$ is a function of the past history of $x_{t'}$ with $t' \leq t$.

One immediate result due to this difference, is that if you have a flat constant input, with only a pulse at time $t$, then the pulse will be smoothed if you use a moving average, but its shape will be kept better if you use SFA. 

You can always try both moving average and SFA for your task, although the moving average requires some input parameters such as window width while SFA does not.