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Here's the thing: for qualifications to be completely portable, they sort of have to be the same. Do you agree with this? This is where more integration would be needed... but weirdly enough, that's exactly what the UK is afraid of!
German degrees were completely different from those here in the UK just 15 years ago. A first degree from Germany took longer than a first degree in the UK (average completion time was about 5 years). When I left for university in the UK, a Bachelors degree wasn't worth much in Germany. I knew I had to get at least a Masters degree to even get a job, if I wanted to go back to Germany. It was mainly the depth of the subject matter that was different. A law degree in Germany, for example, required Latin qualifications, certificates that you have witnessed autopsies a few times (funny stories from friends there - apparently, people lived up to stereotype and puked), etc. ...things you just don't do AT ALL for a British law degree.
I am quoting a British teacher who posted the following on an expat forum:
German teachers are trained in a different way to teachers in England and that is usually where the problem lies in terms of the Staatsexamen and Referendariat (two years' prep service) that gives them "Beamte" status. In most cases, English training just does not equate and therefore anyone coming from England has to jump through additional hoops in order to teach here as well as becoming adept at the German language. It is not impossible but it is very difficult and very rare for a teacher from England to get a job in the German system apart from in state Europaschulen, where they get paid less than the German qualified teachers anyway because of this Beamte versus Angestellte thing.
Giving someone trained as a teacher in the UK 'Beamte' status in Germany is like allowing someone with a simple driving license to drive a huge lorry. I'm pretty sure you'd want immigrants coming to the UK to be adequately qualified, too? Or should we accept someone who did a 1-year course from (insert country) do a job for which a British person would need to complete a 3-year degree?
A few months ago, there was a programme on TV about British nurseries and how they are the most expensive ones in Europe. Now, you'd think that British nurseries would thus have an edge compared to European ones. Maybe better qualified nursery teachers? But when they compared this to France, where childcare is dead cheap, the result was astonishing. The French nursery teachers were far better qualified than the ones here in the UK. So basically, we are paying much more and getting much less. 
Is the UK really that much better than the EU??
But you see, in the last decade or so, German universities have actually been introducing an anglicised system (BA, MA, etc.) with fixed time periods for study. This raised the eyebrows of many, many conservative Germans (who will always think their education system is better, no matter what), but had it happened the other way around - here in the UK - there would have been a proper outcry, with people shouting, "We won't let the EU tell us what to do."
This was done to reinvigorate the German higher education system which underwent a bleak period in the 90s. But honestly - I think they just wanted to shorten the time students actually spent at university. People remaining students until their late 20s / early 30s were not unheard of and very much the norm at the time! This anglicised model has also been popular with the students as their degrees became more globally recognised ("MA in Law" is a lot easier to understand than "Diplom-Jurist")... and it just sounds cooler, full stop.
This change has mainly happened with the more commercial degrees, after which people would get private sector jobs. The public sector (like with anything public sector anywhere) sort of moves like a tortoise though. But things are changing, albeit as with everything that requires the change in the psyche of an entire population... very slowly.
I hope you found this useful.