Well, I can say as much as I know. OK, there are several of them - but some can be misleading. For instance, I think the ones that deal directly with "trust" are light-years more valuable, often times, then Moz's DA (domain authority) and PA (page authority). Anyway, I would look at the "trust" oriented ones first and then the others.
Well, at least one "trust oriented" one is Majestic.com's TF (trust flow).
O.K. why am I harsh on Moz? Well, Moz is an inspiration in becoming so powerful a website, but it's metrics are easily influenced by spam. In other words, someone could raise DA or PA by simply linking to powerful sites, but here's the kicker, which are unrelated to the niche. On top of that, the posts, causing the DA increase etc., could be posted in a spammy fashion (End Result of All This: Sites with high DA/PA but low domain metrics elsewhere).
I don't use them often since I am not dwelling on trying to make a business but I think they are a pretty interesting view on how your website is doing compared to other websites similar to yours, or just by itself, it is good to learn some stuff regarding your strengths and weaknesses.
If you mean using them to see where are the more valuable websites, I would assume it is best not to go just with one of such websites, since they take different metrics and things can be giving you a result that doesn't reflect the current state. One dumb example, but it can serve as an example: I once searched for my old community I used to have and gave me a huge result because my community was a subdomain of a self-hosted service, so the results were that of the service and not my website.
They all have their own way about how they calculate the scores. Majestic is probably the most accurate out of all of them in my opinion but is very expensive to pay for their services just to see some backlinks. If you have a huge site it might be worth it but not so much worth it to me quite yet.
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I haven't used a domain metric in years, mostly since the last time I used it I got conflicting scores. So I was like 'meh' and never bothered with it.
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They all have their own way about how they calculate the scores. Majestic is probably the most accurate out of all of them in my opinion but is very expensive to pay for their services just to see some backlinks. If you have a huge site it might be worth it but not so much worth it to me quite yet.
Well, it would be interesting to "spy on" other site's back-links. That's perfectly legal and ethical - and would give you a blueprint for your own site. O.K. who has done this?