In my experience, through testing with friends, different characters and even Kakashi in a range of situations.
I've never been able to to observe a noticeable difference in damage or effects of any kind with the Nin/Atk *ion stats, the runes still add power but they don't actually seem to affect damage.

Those stats are particularly hard to level up too and we had Red Runes boosting them by over 50% which should be quite significant in some way, but yet no observable difference in damage/fights, so for the time being they seem practically irrelevant.

You can never go wrong with Core Stats + Initiative though, even if they did work, I don't believe Injury works either but I don't remember testing it.