Printed images can be obtained on chemical photo paper (either with a digital illuminator/projector or from a film after enlargment), or from file using printers and modern inks (pigments or dyes).
In the hypothesis of having the same negative film source, and assuming no retouching on the digital path, would I obtain an higher quality result (see below) with chemical print with an enlarger, or by scanning it at a high enough (effective) resolution and printing the digital file with modern techniques?
The three aspects included in the definition of "better" are resolution, color gamut, density (dynamic range), longevity. In summary, I refer not to personal likings but to the attainable specifications (wider gamut, higher dynamic range, higher resolution).
Regarding the types of prints from digital file, I have in mind chemical photo paper with digital illuminator (as high end labs do), but also special photo papers with pigments or dyes.
The three aspects are resolution, color gamut, density (dynamic range). When I say "better" I refer to the technical aspect, therefore "better specifications" (wider gamut, higher dynamic range, higher resolution).
I think that chemical print from film would be equivalent to chemical print with digital illuminator (or better, given the lack of intermediate steps and assuming same chemical paper). However, I don't know how pigments and dyes compare.