I think the project's webpage pretty much sums it up already:
- Find Any File can find files that Spotlight doesn't, e.g. those inside bundles and packages and in inside folders that are usually excluded from Spotlight search. It can even search in other user's folders if you use FAF's unique root search mode.
Find Any File doesn't replace Spotlight, but it complements it greatly:
- If you search for content, such as text in PDFs, Word documents etc., use Spotlight or its alternatives.
- If you search for files by name, size, date or kind, use FAF, because only then you can be sure that everything available is found.
Additionally, Spotlight also doesn't show hidden files, which I don't know if this app does. And anything located in a directory macOS doesn't deem a "user directory" like System folders, are usually not surfaced by Spotlight either, intentionally.