Hello saxena,

You can start preparing for IES as the syllabus is more in IES and it takes more time, for GATE you can work on your aptitude and numericals before few months of GATE examination,

As If you prepare for IES your theory part will be completed automatically and for GATE you can practice numericals so that you can get good marks in GATE.

But it's very important to focus on one of the competition first as you need to get maximum knowledge and learning so that you can get a good rank and get desired job/college.

I hope it helps,

Best of luck