I have applied my ESTA using online web form from my laptop.
My friend has applied for ESTA using smartphone app.
When compared, our experience was quite different. The app has apparently far more steps; it scans your passport and 3D face scan. By scanning passport was meant NFC scan I assume, downloading data from the chip embedded chip in your plastic hard part of you passport, including biometrical data.
In the web app, you only upload photo/scan of you main passport page. Which does include your photo. No taking picture of your face. No downloading of your biometrical data. No need to have passport by your hand, you already have a photo/scan of it.
The smartphone app is not even mentioned on any of the official sites:
https://esta.cbp.dhs.gov/
https://www.usa.gov/visa-waiver-esta
You have open the https://esta.cbp.dhs.gov/ link in mobile web browser and only there you get a button in the page header saying "Open in App" which will take you to the app store.
Would it give one any advantage to have it done by the much more nosy app compared to the more restrained web application?