Step 1: Determine whether the model fits your data
Examine the plot to determine whether your model fits your data. If the fits closely follow the actual data, the model fits your data.
If the model fits the data, you can perform Winters' Method and compare the two models.
Decomposition uses a constant linear trend. If the trend appears to have curvature, decomposition will not provide a good fit. You should use Winters' Method.
If the model does not fit the data, examine the plot for a lack of seasonality. If there is no seasonal pattern, you should use a different time series analysis. For more information, go to Which time series analysis should I use?.
Step 2: Compare the fit of your model to other models
Use the accuracy measures (MAPE, MAD, and MSD) to compare the fit of your model to other time series models. These statistics are not very informative by themselves, but you can use them to compare the fits obtained by using different methods. For all 3 statistics, smaller values usually indicate a better fitting model. If a single model does not have the lowest values for all 3 statistics, MAPE is usually the preferred measurement.
The accuracy measures provide an indication of the accuracy you might expect when you forecast out 1 period from the end of the data. Therefore, they do not indicate the accuracy of forecasting out more than 1 period. If you're using the model for forecasting, you shouldn't base your decision solely on accuracy measures. You should also examine the fit of the model to ensure that the forecasts and the model follow the data closely, especially at the end of the series.
Step 3: Determine whether the forecasts are accurate
Decomposition uses a fixed trend line and fixed seasonal indices. Because both the trend and the seasonal indices are fixed, you should only use decomposition to forecast when the trend and seasonality are very consistent. It is especially important to verify that the fits match the actual values at the end of the time series. If the seasonal pattern or trend do not match up with the fits at the end of the data, use Winters' Method.