Welcome to Android Central! How did you transfer the data, and what note-taking app were you using on your S3? If it was a Samsung app, then it would not have transferred over to your HTC One, since they're different brands. Do you still have the S3, or is it gone?
In the future, it's probably better to use a notetaking app that saves or syncs your notes to the cloud, like Google Keep or Evernote. That way, you can access it on any device or computer.