There have been conducted hundreds of analysis of this exact topic you are commenting on.
As already have been mentioned, these are crawlers, like Google, that exactly try to replicate Google behaviour (except for the caching and ranking on sites based on content).
Tools like SERPstat have proven to be really awesome, even comparing with Majestic and SEMrush at certain stages. They keep improving their crawling algo and since the web is ever changing and many sites go obsolete every day, while thousands are born every day, data is constantly being transformed.
Ahrefs is always known to be in the top of algos. But if you want to do your own research, for every site, just pick all the sites in the linking profile and put them on excel and do your own comparison:
1. Are there duplicates? (for example similar sites with different query vars)
2. Are there much garbage in the crawling (for example those kind of sites that are dead or spammy sites)
3. Are there many pages from different domain, or do they repeat too much for certain crawler?
4. Are the links updated or lost time ago?
You will probably notice, that Ahrefs is the one with more right hits, and semrush is really poor accompanied by Moz (moz tend to be less updated). Majestic somewhere in the middle, but in the last year 2020 was completely wrong 90% of the time so I stopped my subscription (also since I have domdetailer for checking TF and CF I did not need the specific stats from them anymore), but maybe in 2021 they have significantly improved I may check it some point during this year.