I'm an electronic engineer, and feel I could only call myself that after I had completed my 4 year BSc in Electronic Engineering, even though I had been tinkering for years, and studying electronics at school level as well. Afterwards though, it still takes a couple of years to be a productive member of an R&D team. I now have several years experience and I love this job, it never stagnates, always changing and evolving at a lightning fast pace. I'll add though that the basics never change, and are the foundations to everything!
In South Africa, there are generally two types of EE's....Those that studied at a Technikon (Technical college) to get a diploma, and those that go to University for a bachelors degree. Generally anyone who doesn't go those two routes and does something elsewhere would be classified as an artisan, or electrician, unless they spend many years working their way up to EE designation after getting an extremely lucky break at an engineering firm.
From my experience, degree graduates are subjected to a lot of maths and physics, and end up getting a jump start in their career roles as well as earn a higher starting salary. They start in R&D, the real meaty roles and are groomed for leadership, ultimately ending up in management in 15years or so after graduating.
The diploma guys here start off at a slightly lower salary (generally) and get put into more technician roles. It takes a lot longer for them to progress up to the same level. They generally don't do a great deal or any software/firmware development. This limits their progress in an electronic engineering company, because embedded systems are so widespread these days.
This is just from an SA perspective, I'm not sure what its like elsewhere in the world. But either way, if I could give any advice it would be to aim for the highest university level of schooling, and go from there. If you can get a masters then by all means, but that isn't always as beneficial as it seems. Electronics is such a broad field, and a masters so niche, that often that experience means nothing other than having the accolade. Many EE's would probably find it more beneficial to do a masters in some other field, like an MBA or something along those lines.
My 2c