Which Axis cc should I close ?

If you have utility payments covered from other bank credit card then close ACE

Close Ace. Since you're applying for Airtel Axis, your recharge and bill payments would be covered. I understand that 1.5% instead of 1% is a better deal, but it doesn't make a considerable difference unless you have heavy offline usage.

You already have IOCL as LTF, which is a very very good deal. Keep it. And if you ever need to close another one, go with MyZone. For swiggy, I believe Airtel Axis's unconditional 10% is way better than Myzone's 120 off on mov of 500. My first ever credit card was MyZone LTF, but I happy closed it for others since it is almost useless too.

Conditions to close: 

1) if you have other fuel cards like IDFC First power+ then close IOCL not worth it in my opinion

2) ACE you can close once you got SBI cashback or else keep it just for 1.5% offline saving in other cards non supported MCCs as well:) most of the time  and Airtel axis will cover the bills so ya

3) Myzone is not worth if you can get more gift vouchers from trading section ( i am not sure if gift vouchers can be added in addition to myzone offers then its double dip then its good or else Myzone is waste card)

Choose based on your usage

Close ace

Do not close ACE, if u don't get approved for Airtel Card, that would be a big loss. ACE is Precious... Close Myzone

Are you getting paid Airtel Axis cc? If yes, close Ace.

From being one of the best offline cards, axis ace has fallen the cliff.