I believe that EESTEC is complementary to the official education provided by the university. You get to learn a lot of things from organising an event to managing teams to achieve a goal. Additionally, you share your experiences with other like minded people, so in the end you make some good friends. It offers a great chance to learn and experience things in a European level in such a young age.
I was involved for several years in the activities organised by EESTEC, but I believe that the most significant position within LC Athens for me was that of a trainer. That meant that along with other EESTEC trainers, we were organising soft skills trainings in a variety of topics, like Leadership skills, team management, creative thinking etc.
The last few years, graduates of ECE have a variety of fields they can work on. These include (but are not limited to), computer science related jobs (programmer, web developer, hardware engineer, etc), analysts, technology consultants.
The department has a significant amount of courses closely related to Maths, Physics, so a strong background is required. Also, the program in NTUA focuses more on learning patterns in the problems an engineer need to solve rather than getting to know the x/y technology you will need for a job. So, if for instance you want to become a web developer and you are absolutely sure about it, then maybe this department is not the ideal place. However, personally I gained a lot from learning to recognise the patterns and the broader perspective of a problem.