GATE is purely a technical examination focused on the stream in which you have done your graduation. GATE is used as the entrance criteria for the post graduate courses at IITs, NITs and other engineering colleges across India. It is also used for recruitment for Government organizations (PSUs)such as NTPC, ONGC, etc.

GRE is primarily for pursuing M.Tech/MS/Ph.D programs in abroad as well as in India(for some colleges) and consists of the following sections - Quantitative Aptitude, Verbal Reasoning, Analytical Writing ( Issue and Argument based). There are no technical questions in the GRE exam as with Gate you can get admission in Indian universities as well as few universities of Germany. With GRE you can get admit in USA, Canada, Australia etc.

So I would suggest you to read out all the points given above and also consider your interest and potential before making any decision.

Good Luck!!!