1) Skill type matters. prompt-type will always go first compared to non-prompt skills(barriers etc) , unless you do delayed key pressing.
2) Order matters. higher order ninja will always go first regardless of initiative, as long as both skills are of same type.
3) Even if both have same refine and same rank in battle armor, maybe someone has progressed a bit more on armor rank than an opponent. We get small buff in stats and refinement almost everytime we use threads to fill armor rank. Maybe your friend has little edge here? even 1-2 difference can matter.

Although, if both have exact same initiative, same prompt skill and same order - then I'm not sure how its calculated. Maybe someone else can confirm about it. This post was last edited by Sourav at 2016-10-20 09:54

Strange. only explanation I can make is maybe its due to network issue, but this doesn't sound convincing..

Me and my friend did a test today. Both of us are fire main, both have exact same initiave value on the ninja we are experimenting. Here are the results, was quite interesting, atleast to me.
Test 1: I have tobi in order 1 and he has main in order 1. We both have exact same initiave on tobi/main. In round two, if both of us press mystery skills at the same time, tobi will always go before main. Did it a few times(with pressing hotkeys from the end of round 1) , always same result.

Test 2: Now, I put kakashi in order 1 instead of tobi. again, both of us have exact same initiative on kakashi/main. Now, his main will always go before kakashi.

I wonder if there is a hidden mechanism to decide these things when both have same initiative value. If someone else can clarify these, it'd will help a lot.