I disagree that you should go with the calories burned on the elliptical. Most exercise machines are set to record more calories than are actually burned; typically, unless it's very new and sophisticated, it wouldn't have asked for your statistics, whereas when you signed up for the app, you did enter all that information. The app will be more realistic.
No it isn't better to go with the app.
You probably tell your elliptical your current vitals like weight, age, minutes, and resistance. This provides a more accurate caloric burn number than the app in my humble opinion.