Could anyone explain the difference between the datas stored in oo_.SmoothedVariables and in oo_.FilteredVariables generated after bayesian estimation?

Which one should be considered as model generated data (to compare with actual data)?

You have a data sample from 1 to time T. Filtered variables for each time t are estimates from the Kalman filter using data up to time t. In contrast, smoothed estimates come from the Kalman smooether and use the whole data set up to time to T. Smoothed variables are time t thus use all the information in the sample.