Gate (Graduate Aptitude Test in Engineering) is an entrance test which is totally a technical exam for those students who wish to get admission in M.E/M.Tech within India and who wish to get recruited in PSUs. Also, students who are in final year or pass out can give this exam as the syllabus would be the same which they have studied in their B.Tech/B.E. GRE (Graduate Record Examination) is a standardised test which is accepted for admission in various disciplines at many post graduate programs across the globe. Students who wants to pursue Master's degree, specialized masters course, MBA or doctoral degree can sit in this exam. Also, it is not related to any technical subjects as it only consists three sections - Analytical Writing, Verbal Reasoning and Quantitative Reasoning.

Apart from this, if you talk about the best option then it depends on you like what is your interest, potential and which one is more convenient to you. Also, if you want to stay in India then go for Gate and if you want to go abroad for your higher studies then you can give GRE.

Also, to know more about both the exams you can go through the below links as well and let me know if there is any doubt -

All about Gate

All about GRE

Hope this helps!!!