Are you in survival trial?

I see then it's something else. If it's equal then it will pick at random, i tested this with friend for a good few times and it seemed to be about 50/50. If he is going first every time, he is probably higher, even if he is higher just by 1 it still counts as higher.

Nah it's not that, guy i tested with had same refines on move 1, but lower on other 3 ninjas, but who went first was still 50/50, just down to rng.

I think he must have more thread used in his battle armor rank, so even though you are both same rank, he has just few points more or even just 1.