This is really a nice question at the right time. We have several months to go for GATE and probably the same amount of time for GRE, if we decide to take a master degree abroad. I will try to shad light on both the options and let you decide what is good for you. We are trying to understand them because both lead to Master degree in Engineering.
Let me start with GATE, it based on the subject we learned during graduation (BE or B.Tech). GATE exam helps in getting admission in M.Tech (master of Technology degree) in Indian universities.
The basic advantage with GATE is that if you do well you will get to see most prestigious engineering institutes in the world. You get a scholarship to support education and get wonderful two years of life that you are going to remember for rest of you life. Even if you little less scores it will take you to some college where you will enjoy scholarship and time.
The real daunting task comes when the master degree is finished. IITs, NITs and some good universities have placements and everyone have to face huge competition. Even top multinational companies one or two candidates out few hundred bright candidates.
Another disadvantage, because of high competition, is that somehow one need to remove few candidates to make selection procedure to finish in given time, and usually CGP or percentage will come into picture as a short listing criteria killing many bright students who didn't cared much about scores and marks.
Now let's move on to GRE, it's really exciting to go aboard, specially for Indian students. That motivates many students for preparing for GRE. The biggest advantage studying abroad is that the exposure and huge confidence one gain in life. It also depends on where you study. Given a chance to me I would try studying abroad at the earliest age at a best place 
Preparing for GRE need extra effort as English is not our first language, though most of Indian student do good, but one the average we don't do good in English. Apart from this, after GRE, one has to run around a lot to fulfill many other admission requirements. This may discourage few students from taking this option.
The other disadvantages are, if you don't get a scholarship you may land up serving tables in an Indian Restaurant. If your university is not well ranked and you don't have a scholarship then it's totally a mess, one or the other day you will land in India for good too.
Now, if you ask me what I did, when I was standing as a B.Tech final year student? I opted for GATE. But on the same time I tried a lot to understand the admission procedure in Australia, New Zealand and Canada. I did it because there was a useless procedure for paying GRE and TOFEL Fee, I was not good at English and was from a small town and was afraid to go to a metro city and talk to consultancies.
On the other hand, I was good at engineering subjects that made me very comfortable with GATE. Scholarship, and the energy to see IITs was enough for me to opt for GATE. I know my country well and I know the English they speak so all these made GATE easy and best possible option for me.
The most important factor for not going ahead with GRE was lack of guidance and motivation for studying abroad. Paying fee for master degree and managing living in US or other countries was considered as failure at my home. Most of my friend went there either paid full fee, or got some weaver from university and I never saw anyone got scholarship that pay their living there.
After doing M.Tech I started thinking of PhD abroad, but there was again lack of guidance and this time I approached few consultants and they shown a lengthy procedure, which was almost infeasible for me to try. I left that option in their offices and moved on with simple and long loved dream of IITs. The more trouble I saw going abroad the more I loved IITs and became disparate to join there for PhD. Long back I wrote about it
I know where I was going and know what I want to do, and was doing it happily, because of the freedom it offered me. If we don't know what IITs are for then we will end up in books and finally feel that there is always some smarter than you. I got a huge advantage being an IITian. I also, got a chance to visit Singapore and Korea for research without spending a single penny from my pocket.
After spending several years abroad, I feel its better we start early in life. If possible go abroad for engineering degree itself, gain that exposure and try to be best and learn how common people use resources to build big business. Make a point to learn how opportunities come and how to grab them to grow higher.
The conclusion is wherever you go, try to reach excellence and try to be best. Not just say that work like that. Raise above all excuses and work hard to the human capacity and expect the best of it. All Indian you see on the top are because of their hard work and too much competitive and never give up attitude. Let's work hard and chase our dreams.
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Wish you all a wonderful luck ahead.
