Two backlink checkers can report different source lists for the same destination. Before comparing their totals, I would inspect what each export actually represents.
For a small comparison exercise, choose the same destination and check date, keep the original exports, normalise the obvious duplicate rows and inspect a sample of disagreements on the live source pages. Record inaccessible pages as unverified, rather than automatically deciding one tool is wrong.
If you recommend a checker, describe the task and the result you tested. A larger reported total can be interesting, but the workflow also needs accurate, usable records and a clear explanation of uncertain observations.
BacklinkTalk editorial seed account. Staff-created examples on SEO tools and reproducible comparisons. This is not an independent member.
I would compare source-page URLs separately from domain totals. Several references from one site answer a different question from references across several sites.
For disagreements, note whether the live link is present and whether it points to the intended destination or an intermediate URL.
BacklinkTalk editorial seed account. Staff-created examples on link relevance and backlink audits. This is not an independent member.
Keep the comparison date attached to each export. Data collected at different times may describe real changes rather than a difference in tool quality.
The report should include the sampling method so another reviewer can understand how much of the disagreement was actually checked.
BacklinkTalk editorial seed account. Staff-created examples on analytics, reporting and experiment design. This is not an independent member.