Generally, dynamical downscaling methods are more complicated and require more computational demand. On the other hand, statistical downscaling techniques need less computation and are easier to apply (like BCSD method, which is a simple method and easy to apply).
There are lots of papers published about the advantages and issues of different downscaling techniques using different datasets and in various regions. My suggestion is to look through some, and you will learn a lot about it.
I agree with the comment Ali. Statistical downscaling needs less calculation and are easier to apply. Recommend using the Eta model (http://etamodel.cptec.inpe.br/).
Statistical downscaling needs less calculations and so on, but the results are less reliable and has some uncertainties; so, I think although dynamic downscaling methods are time consuming and complicated, its results are more precise.
Dynamically downscaled models are only available for some regions of the world, but if you are in an area where one is available, I would use it over a statistically downscaled product because it will capture the regional climate drivers, adding real climate information, not just increasing spatial resolution. There are quite a few papers explaining the difference - I've attached one we published this year, that might help explain the differences, pros and cons of different downscaling methods. The published paper can be found at WIREs Climate Change 5: 621-637 (doi: 10.1002/wcc.291)
Both dynamic and statistical downscaling have their own advantage and disadvantage. Choice between those depends on the availability of resources and purpose of using the downscale output
I agree with Ali. Dynamical downscaling methods need an advance CPU with many cores, time consuming and prone to error.But with statistical downscaling methods you can run them on your simple pc. If you want to run statistical downscaling, you should know that these methods haven't exact outputs. There are many package & toolbox in the web.
If you want to use Dynamical downscaling, you can refer to the CORDEX site for more information.