In feedback and promo docs my leadership and soft skills were called out as exemplary and distinctively strong.

If anything it's the opposite. I don't think my technical skills are as strong as some peers at my level. A big part of the difficulty is that the other engineer is more experience in certain technologies than I am. I'm self-aware enough to recognize those cases, and don't try to override him.

Seems like your company has an issue with avoiding tough conversations? How much do you trust the feedback you got?

If your soft skills are so good why are you getting bodied by this guy?

If your are such a great leader why are your reports siding with the jerk?