A couple years ago I wrote an article that may help:
https://moz.com/blog/going-beyond-moz-metrics-to-answer-why-is-this-site-outranking-me
(I disagree now with a few of my own ideas of what else may matter ... but the idea remains the same.)
Metrics aren't everything and can be skewed by things like volume, spam, and things that affect ranking that have nothing to do with link metrics. Keep in mind - link & domain metrics are one small part of ranking. Age of the domain, website speed, content of course ... all these things could play into rankings.
What does the content look like? Page titles related to KWs? H1 & H2s used similarly on both sites? Duplicate content on one?
Just keep in mind that these metrics are just a piece. You wouldn't think you bought a car if someone just handed you a steering wheel, right? Check the tires. Check the engine.
