Advantages and disadvantages of doing a PostDoc Maybe the answer to this question varies depending on the field of study. I am asking it from an Engineering perspective. I am currently enrolled in a PhD program in Mechanical Engineering (carried out with an industrial partner) and would like to join a research department in the aeronautical/aerospace industry.

For PhD students in a similar situation, what would you consider to be the main advantages (and disadvantages) of doing a Post-Doc ? Should you target a better ranked university than where you did your PhD, same level or lower ? or should you rather join industry straight after finishing the PhD ?

Feel free to share your thoughts and experience. There's probably multiple answers to this question.
I have a situation somewhat related to yours: I did a PhD in engineering with an industrial partner, and I'm now a post-doc researcher in a reputable university. It sounds, when you say 'doing a postdoc', that you have the impression that it is the logical 'next level' in the sequence: bachelors - masters - PhD - … but it is not. 

There are no 'advantages' or 'disadvantages' in being a postdoc researcher for a while. It's just that, with some rare exceptions, you will not get a faculty position right after you graduate from your PhD. 

The time spent as a postdoc is usually the time where you gain experience, hopefully make your peers aware of your existence, publish (or finish publishing) the chapters of your PhD thesis and maybe that study that you feel will make you stand out, etc. in other words: giving yourself the pedigree that will make you interesting for an academic hiring committee. 

Since you have no intentions of becoming a professor, there are no real reason to 'do a postdoc', unless there aren't any other options (which I assume is not the case for you, as an engineer with experience in translational research/industry).