The preference should be firstly based on the branch and not on the colleges. Opt for the college where you get the branch of your choice. It's not college that matters but rather it's the branch. If you get the branch of your choice, you will be more likely to study that well and attain a successful future. 

• If you are more into the programming languages, the technology and are passionate about learning the subjects associated with the CSE, then opt for GEC as there's nothing above the branch. 
• If you have an interest in EEE, opt straight for the NIT Goa as it is an institute that will never disappoint in terms of placement, academics, faculties, or higher studies. 
• NIT Goa is a brand in itself. But opt for it only if you are sure about the branch.

If you think that you will take EEE in NIT Goa and then change the branch to CSE, then it's nearly impossible. There are high cut offs for changing the branch and it happens after following a certain set of rules that is not possible. So choose wisely as your career depends on it.

Before diving into any conclusion, it is important that you understand the basic difference between B.Tech and B.E degrees. Following which, you have to clarify the doubts you have regarding both NIT Goa and Goa Engineering College.

• If you weigh the general brand value that arrives with the NIT tag, you will then already be more exposed to the industrial demands and explore better opportunities at NIT.
• However, there has been a genuine depreciation at Goa Engineering College. 
• You can possibly go out, looking for particular job offers after the completion of the B.E degree but you will obtain better placements by the college cell itself. 
• When talking about the faculty, there are several Ph.D graduates from most of the top institutions who have been teaching at NIT Goa. 
• The highest salary package was 16 LPA at NIT Goa. 
• On the other hand, at GEC, you might or might not secure placement. 
• Their highest package sometimes does not reach even up to 7 LPA. 

Therefore, it is suggested that you opt for NIT Goa, as it will provide you with better opportunities. They have an active placement cell, which not only helps with placements but also conducts seminars, internships and industrial visits.

It is suggested that you choose the institute that is in close proximity to your location, since both the institutes are rather tier-3 Indian Engineering Colleges. 

• The major similarity both Goa Engineering College and NIT Goa share is that fresh graduates often go on to become clerks at several service based companies. 
• They often get an average salary package ranging anywhere between 3 LPA to 4 LPA.

In any case, nobody can apparently have access to the actual placement report of either institute because most of them generally spike their records for unjust purposes. Yet, here is a detailed placement statistics, as is claimed by the institutes in general.

Indian students generally should enroll at colleges near to their residence. And later start to impel the administration to offer basic amenities, if any missing, thereby gradually incrementing the possibility of them obtaining industry relevant skills. Your placements and overall college life has to provide you with the necessary facilities, only then you can grow as an individual.