Hello, I hope you are doing well

Before asking about what branch is better for giving GATE, you should know that if you are targeting for Govt. PSUs you can't get into them regardless of the branch you give gate in, because only B. Tech in ME students could get the opportunity to work in PSUs. You can still try your luck though.

Also, you should see where your interest lies because at the end you would have to do M. Tech in that course only. GATE through PI is difficult because you will have to get a very good rank (AIR 30-50) to get into top IITs for M. Tech or else you will end up in newer IITs.

Hope this helps.