async-await.js

async storeAccountInfo(username, password) {
  await storage.ready();
  await storage.set('username', username);
  const cleanup = [];
  if ((await touchId.encrypt()).withFingerprint) {
    const [, secureStorage] = await Promise.all([
      storage.set('usingTouchId', true),
      secureStorage = await secureStorageFactory.create(),
    ]);
    await secureStorage.set('password', password);
    cleanup.push(secureStorage.close())
  }
  cleanup.push(storage.close());
  await Promise.all(cleanup);
}

promises.js

storeAccountInfo(username, password) {
  const cleanup = [];
  let secureStorage;
  return storage.ready()
  .then(() => storage.set('username', username))
  .then(() => touchId.encrypt())
  .then(touchIdResponse => {
    if (touchIdResponse.withFingerprint) {
      return Promise.all([
        storage.set('usingTouchId', true),
        secureStorageFactory.create(),
      ]).then([, _secureStorage]) => {       
        secureStorage = _secureStorage;
        return secureStorage.set('password', password);
      }).then(() => {
        cleanup.push(secureStorage.close());
      })
    }
  })
  .then(() => {
    cleanup.push(storage.close());
    return Promise.all(cleanup);
  })
  // the other example has no `return`, so this promise chain should
  // return nothing to be consistent
  .then(() => {});
}