There are a lot of SEO tools out there and many of them are exceptionally competitive but AHrefs is always my go-to tool when I'm not using more than one.
One of the things that AHrefs is best at is helping with a content marketing strategy. Though it's best known as a backlink index (which it's great at and I'll get into that), coming up with good content ideas is one of the things I get the most use out of it with using the content explorer. I find articles that do well for the topics I want to target and it's clear what already resonates with your audience which is powerful.
The backlink index is one of the best too though at the time of writing, Moz has just improved their index. Regardless of index size, which theirs is large enough, the type of data they provide is the most useful. The broken links data is probably the most useful that isn't easily matched by other tools. Additionally, going back to the content explorer, you can find unlinked mentions, a feature that appears to have been removed in Moz's "new" tool (I may just not be able to find it).
The rest of the tools are generally matched by other competitors to some degree though, in general, AHrefs understands what you intend to do with that data and presents the most useful information first.
The only feature that seems to "lag" compared to it's competitors is their site audit tool. This only launched a few months ago but in my experience experimenting with this tool, it's not the most effective.
This is probably the best tool for content marketing, link building, and third party keyword research. If your primary concern is tracking technical errors this tool is alright but probably not the best
I'm the biggest AHref's proponent in my agency, we do use the other tools but the biggest benefit that we get is more accurate data to cross-reference with other SEO tools.