Pen to Print is the most recognisable dedicated handwriting app, with a long track record and a large review base on both mobile stores. Its "Cursive Reader" is aimed squarely at connected handwriting, which is where most general scanner apps fall apart.
We did not put it through the scanned-page WER harness because its natural input is a phone photo rather than a comparable 300 DPI scan, so a head-to-head number would not be fair. In hands-on use it is clearly better on cursive than the built-in phone tools, and clearly behind the specialist web services on messy or faded pages.
The right way to think about it: if you want an app on your phone for tidy, occasional notes, this is the one to pick. If you have an archive, need an API, or are working with difficult historical hands, a specialist web service will save you more time than the app convenience is worth.