checking DA of couple of websites on Ahrefs and Other tools like small seo tools..
DA on other tools - 14, 16
DR on Ahrefs - 2, 3
which one should be considered or is there other tool to check DA
You are taking these score in wrong way. Let me try to correct..
Different backlink audit tools like Moz, SEMrush, Ahrefs, Majestic etc. keep crawling the backlinks to offer their SEO backlink audit and competitor audit services and have created their own metrics to give users a score based on the backlinks data that they have gained. Here is a brief overview of that -
DA (Domain Authority) and PA (Page Authority) are used and provided by Moz
DR (Domain Rating) and PR (Page Rating) are used and provided by Ahrefs
AS (Domain Authority Score) is used and provided by SEMrush
TF (Trust Flow) and CF (Citation Flow) scores are used and provided by Majestic.
Various score checker tools like Small SEO tools, have to use these backlink audit tool's APIs to provide that score. So if you see above metrics in any other tool (like checking DA in Small SEO tools) then the score still belongs to Moz as its coming through their API. And if you want to check particular score most accurately then check in the main tool itself like check DA in Moz, DR in Ahrefs and so on.
Different score in different tool - it is obvious because these tools have different source of backlinks data and calculation of the score is also different in each, they all crawl backlinks separately and create own database. None of these backlink audit tools can crawl entire web and so not able to find all backlinks that a website have on internet. They can crawl only a small portion of it and their score is also based on that.
Which one should be considered - Google do not consider any of these tools. Google has its own algorithm to find the authority of a website and have largest crawled data of webpages as well. These third party scores claim to show the ability of a website to rank in Google but in actual they can not. You can't rely on any particular tool as their data is limited and these tool scores can be manipulated too.
You can just use these scores while comparing your website with your competitors and for that you can consider checking in as much as tools so that you can get a broad view of the worth that particular website have.