GRE and GATE are required to go for similar courses but that there is some difference between them. Let me elaborate on the advantage of giving GATE first and then I will talk about GRE.
Its way cheaper and costs literally 10 times less than GRE
allows you to pursue M.Tech from the Indian colleges like IISc, IIT, NIT, etc and it is also used for getting placement in PSUs(You need to be a top performer for cracking a PSU Job via GATE but some people do get it.)
Finally, GATE in itself is enough to get admitted in a top college in India for higher studies in technical branch and doesn't depend much on anything else apart from your GATE rank.
GATE scores are valid for just 1 year so if you do give GATE, you better be sure as to why you are investing time preparing for such a tough exam.
The GRE is an international competitive examination which is not just taken by Engineering colleges, but unlike GATE, you can even apply to B-schools with your GRE scores(few B-schools are there which still require GMAT ) So if at any point in your life you decide that you want a change of career, and want an MBA or MIM from a top program abroad, you can use your GRE score( GRE scores are valid up to 5 years, so yes it is possible you can decide 4 years later and give GRE now)
GRE is useful for those students who want to kick start their career abroad, may it be MS, MBA or MIM. You get to apply to the best institutes in the world. ( As we all know that IITs are good and well renowned, but given a chance to study at a top 20 MS program from the likes of Harvard, Olin, Stanford, etc to any student, the sane ones will choose the latter in a heartbeat :-p) The merits of MS abroad to that of Indian MTech is not an topic of debate and I leave that for some other day.
GRE is costly, it requires somewhere around 13k-14k to sit for an exam. Then comes the non-refundable application fees that you need to pay for colleges along with application package, and they can be easily in the range of 8–12k per college. So yes, you need to be able to sustain that initial 50k or so by yourself.
Now to sum it up, the decision is individual-based. If you want to study and work in India only, then its better to close your GRE books and get started with GATE. But if you want to break the conventional chain, add that international flair to your career, work and learn in new cultures, and yes, earn hefty packages.
Both options are good but it depends on individuals according to their career interest. Do your research, understand what you want to do in life, take your time, and only then go for investing your time and money for masters be it from India or Abroad.
Hope this helps.