Yoast isn't mentionable with the others...
Most guys talk a lot about Ahrefs like it's the greatest thing ever, but the fact of the matter is that DA/PA is still the universal standard of domain metrics.
It depends on your use-case, because Ahrefs has a great keyword utility, for example, and supposedly a larger database, but Moz also has some features that Ahrefs doesn't have.
With Ahrefs, you can see quantity of keywords ranking in the top 100, for example, and they have traffic estimations, and a great viewable for various metrics in the same on-screen spreadsheet.
Moz, on the otherhand, has a Spam score, which Ahrefs doesn't even offer, and the UI is sort-of broken-up into sections, which isn't as good as how Ahrefs lets you view everything.
Moz has the core things that you need, like spam score, top 50 rankings, DA/PA, Referring Domains and Total Links, but it's missing a lot of the granular metrics that Ahrefs offers.
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I'm tempted to say that Spamzilla is better than all of them, simply because you can view multiple metrics from the same dash, but the scale is also very low, although the price is much lower, as well.
DomDetailer is a cheap solution for basic metrics from Moz and Majestic, but you don't get a spam score or keywords ranking, which I think are essential metrics for link-building.
SEMrush is overpriced, but it's got great features for looking at traffic, and analyzing competitors.
It's more of a suite of tools for marketing, rather than just focusing on SEO, though.
Majestic has a great way of presenting their core metrics, which I think is more insightful than the other core metrics, frankly, but without spam score or ranking keywords, none of them can be viewed by themselves.
They also show topical tagging estimations for URLs, and languages, which is super useful for determining cleanliness of the link profile.
Majestic is also really a bulk link analytics tool, so it's really just a one-show pony.
I'm a big fan of the dash offered by SE Ranking, although they base their data on Moz.
Also, SpyFu, I think is really underrated, because their viewables make everything really easy to understand.
They are a much smaller database, but they are much cheaper, and the insights, I think, are actually superior in some areas like with keywords, but they also lean a little towards PPC.
At the end of the day, it's mostly about your KPI dashboard layout, pretty much, rather than the underlying data.
Both are important, in reasonable levels.
There are videos out-there, where guys compare majestic metrics to ahrefs, and fawn over how amazing ahrefs database is supposed to be.
I'm sure there's an argument to be made, for each independent feature.
I think the best solutions for the dollar are:
1. SE Ranking
2. DomDetailer
3. SpyFu
4. Majestic
5. Spamzilla
6. Ahrefs
7. SEMrush
8. Moz
They each have their benefits, but I don't think there's a single tool I would recommend over any other, necessarily.
In my current group buy stack, I use a few of these for various processes.
Surprisingly, multi-million dollar companies, like these, are not doing a very good job in terms of understanding what is important from a dash perspective, or in terms of correlating data properly.
The most well-rounded solution is probably SEMrush, followed by Ahrefs, and everyone else tends to have a specific focus.
Smaller versions would be SE Ranking and SpyFu... both of which, I think, are extremely underrated, by comparison.
You can use free mozscape api credits to get the occasional spam score you might need, but otherwise, it doesn't really offer a lot, despite being the age-old standard.
So, if you're spending around $35/mo, then either SE Ranking or SpyFu will serve you well.
If you're spending around $100/mo then either SEMrush or Ahrefs would be the better choices.
If you don't wanna invest a retainer, then DomDetailer, and free Moz usage is the way to go.
You can get everything with group buy trial accounts, pretty much, as well.
I dunno everything about all tools, but I've used many of them at one point, or another.
I'm always open to a better tool.