The Welles Wilder Smoothing indicator reacts slower to the changes of the price in comparison with the Exponential moving average. It gives you the qualities of an Exponential moving average, with some what reduced sensitivity to price changes.Because it is less sensitive, it might avoid potentially false signals the Exponential Moving average wouldn't.
The Welles Wilder's Smoothing indicator is similar to an exponential moving average. The indicator does not use the standard exponential moving average formula. Welles Wilder described 1/14 of today's data + 13/14 of yesterday's average as a 14-day exponential moving average.