ARIMAX vs VAR comparison With a time series Y of interest and another time series X that possible explains a part of Y, I came up with using ARIMAX and VAR models to model. 
What is the difference?  
Thanks,
 A: From a theoretical perspective, VAR does not include moving-average (MA) terms and approximates any existing MA patterns by extra autoregressives lags, which is a less parsimonious solution than directly including MA terms as in an ARIMAX model. On the other hand, VAR can be estimated using OLS or GLS which are generally fast, while ARIMAX requires maximum likelihood estimation which is generally slow.
Whether VAR or ARIMAX provides a better representation of the underlying process in your application is an empirical question. You could try fitting both and doing some validation. E.g. construct a rolling window within your sample, fit a VAR and an ARIMAX model in it, and predict one step ahead. Roll the window all the way, collect the one-step-ahead forecasts from the two models and compare their accuracy. The model generating the higher accuracy is to be preferred.
Rob J. Hyndman has a brief note on ARIMAX and related models in his blog: "The ARIMAX model muddle", perhaps it will be of help.
