> A hand-rolled recursive descent parser can say something like "missing semicolon after return statement" because the code knows exactly what construct it's in.

> A generated parser's error is usually derived mechanically from the state machine, "expected one of: X, Y, Z, got W", which is correct but generic.

You are not describing the difference between hand-written and generated but rather top down vs. bottom up.

There may be some confusion here because hand-written parsers are almost always recursive decent (a form of top down), while the most popular parser generators (yacc, bison) are bottom up. However hand-written bottom up parsers do exist (Pratt parsing, recursive ascent), as do top down parser generators (ANTLR, Coco/R, Chumksy). Chumsky in particular gives pretty decent error messages out of the box.

Bottom up parsers can parse a larger set of languages than top down parsers, but the tradeoff is you don't know what you are parsing until you successfully reduce the rule (unlike top down parsers). This is why errors in bottom up parsers often lack comments on structure/context like "after return statement" and can only give a list of which alternative symbols would have been valid.