1. If the app doesn't have permissions to use the internet (possibly Android only, although the Android 6 discussion seems to suggest that there's ways round this).
2. If you use the app while disconnected from the internet and ensure that it isn't running when you reconnect.
Neither of those is possible when you upload the image to be parsed online.
Those are both hypothetical that are very far from typical ways that people use apps on their phones.
An app might upload the image to a remote server. A website might parse it locally through JS - maybe disabling your connection, submitting your image, parsing it, then wiping your cached website data would be just as "safe".
The problem is the knee-jerk reaction that "some random website" is dangerous while some random app is not. You have to assume both are equally risky in this situation.
1. If the app doesn't have permissions to use the internet (possibly Android only, although the Android 6 discussion seems to suggest that there's ways round this).
2. If you use the app while disconnected from the internet and ensure that it isn't running when you reconnect.
Neither of those is possible when you upload the image to be parsed online.