Sore point with some people. As you said, the whole idea of this free trade and free movement charade was supposedly to enable people to go to any EU country and live and work on the same terms as a native of that country, with extra things like recognition of other member states' qualifications thrown in to make the task easier. In theory, there was also the wonderful-sounding idea that for "fair play" the restrictions in one country should not be any greater than those in another.
Just make some inquiries about doing this in practice though, and you soon realize that the bureaucracy still wants you to jump through loads of hoops like applying for a residence card, registering for things which may not even exist in your own country, and so on.
According to all the literature, the govt. of an EU member state is obliged
to recognize the equivalent qualification of another EU country. There is some govt. organization here (I forget its name) which was set up to assess foreign qualifications and issue a U.K.-equivalent certificate. Presumably there are similar offices in other EU countries.
By the way, they operate with non-EU qualifications as well, and when I asked about a U.K. equivalent of U.S. certificates they replied that they couldn't help due to the specialized nature of the subject matter involved! Now if I'd asked about U.K. equivalents for an Outer Mongolian qualification in sheep herding, I could understand it, but we're talking about American electronics certificates here.