Hi Matt,
I can tell you that Google does not value multiple links from one domain, so if I get 40 links from example.com, it will not count nearly as much as if I got 40 links from different domains.
It looks like you have found a place where you have followed backlinks.
Because of the lack of RD's or backlink diversity, you would not be able to distinguish really if one site is all that much better from the back links perspective. (Without seeing the backlinks)
Then the other they're both really not the way you want Google to judge your back link profile based on such little diversity.
Something that leads me to believe he has more relevant or powerful backlinks. Please do not think I'm saying something negative I do not have all the information so I can only tell you what I think based on what I have been shown.
Meaning RD's And unique IP's are what matters not a bunch of links that for all they know could have been your buddies site how relevant are your backlinks and how established or how powerful are your backlinks that are from different domains compared to your competitor?
It seems based on the authority rankings that your competitor has more relevant or powerful back links. Think of it this way if I were in finance I would rather get a backlink from Bloomberg.com or Forbes.com then Moz.com however I would prefer backlink from Moz.com only because it is more relevant unless one of these magazines was doing a story on me and, therefore, making it suitable.
Every example I've given you is a very high domain authority URL. If I got 40 links from every one of them, it would not help me very much. Where if I got ten links from unique domains it would give me a hand much more.
Relevancy so if I have one link verse your 20, and I will take my one relevant link from a high authority domain verse I ton of these less powerful domains.
I'm not saying that you are thinking from bad domains I'm just saying that the statistics that you're giving me are not something that is surprising. You both have very few root domains it would have to be that this person has more relevant or more powerful root domains.
If you feel comfortable showing us your back link profile in their back link profile, I'll be more than happy to explain precisely what I mean.
Please understand there are a lot of moving parts and were just talking about page and domain authority not the other big players like brain rank.
I hope this is of some help,
Tom