If one speaks about usefulness, one must always ask: useful for what?

VAR models are not economic, but statistical methods which can be applied for forecasting economic variables (but can also be applied in other scientific fields). Often, there is no explicit explanation of causalities, and if, the main weight is mostly on statistical fit than on economic content. Nevertheless, at least for short-term forecasts, VAR methods are likely to outperform other models.

DSGE is clearly an economic model and need not have to do anything with statistics. In general, the parameters of the numerical models are calibrated by the authors in order to get somewhat reasonable results. Many DSGE modellers would not pretend that their model is good for short-term forecasts, but would stress that it shows a long-run development. I find that the (principal) assumptions of the usual DSGE model are too unrealistic (not to say antirealistic) to make the model useful for any purpose other than to spread neoclassical ideology.

Dear Rantu

Please look on some papers which may be useful for you

https://ideas.repec.org/h/eee/monchp/3-07.html

http://www.sciencedirect.com/science/article/pii/S0165188908001838

Bests