Should I manufacture my product in EU or in Asia?

This depends on what your values are, what you are trying to achieve and the type of parts you wish to manufacture. Manufacturing close to home always has the advantage of it being nearby, which is great when you are manufacturing things for the first time when a lot of things still go wrong. Communication is of course a lot smoother as well when still in development.

There are some myths concerning the fact that Asia is always cheaper. For some manufacturing techniques the cost advantage of Asia is decimated by the shipping costs and with others there is hardly a difference between EU and Asia.

But if you are looking for speed, diversity in manufacturing techniques or require a lot of manual manipulations of a part, Asia is hard to beat. But be very careful if it comes to quality and communication. Be sure to make clear agreements and ideally have a local contact check out the factory (or go see for yourself). There are also agencies specializing in this type of supplier sourcing, furthermore, there are a lot of European manufacturers that own and operate factories in Asia. These are especially interesting, but make sure they actually own the factory and are not just outsourcing.

At the end of the day there is no wrong answer here; but be sure to thoroughly investigate your suppliers and beware of shipping costs.