Say plainly what it is
Semantic Scholar is a public good. The Allen Institute runs it free, at a scale no startup in this category matches, and publishes the API openly. Several products compared elsewhere on this site are, underneath, a wrapper over it with a nicer interface.
Lune is not one of them. It builds its own index from venue proceedings and parses the full text, which is the reason it can quote a paper rather than describe one.
The layer above metadata
The public API returns records: titles, abstracts, authors, citation edges, TLDR summaries. That is enough to find a paper and to build search on top of, which is why so many tools do.
It is not enough to answer whether a paper supports your sentence, because the answer is in the body. Lune indexes accepted papers in full, so verify_claims returns the line and get_paper_fulltext returns the section.
When free is simply the right answer
If you need breadth, or you are building on a budget, use Semantic Scholar. Nothing on our pricing page beats free from a non-profit, and pretending otherwise would insult you.
Pay for Lune only when the gap it fills is one you actually feel: quoting the source, checking a draft, comparing methods across papers you name.