I was going by heart rate since you mentioned the Polar heart rate chest strap.
Polar app might say 500 calories (the strap itself doesn't tell you calories burned).
Treadmill might say 200 calories. Endomondo might say something else. MapMyRun might say something else. The bike at the gym might say something else. The Watch might say something else.
You're gonna return the watch because the calorie count on apps differ?
If you (or your wife) knows that she was in the heart rate training zone for X minutes during a workout -- then that should be what matters most. Who cares what the calorie count on an app says? They're ALL estimates and they're all going to be different.
In my experience -- heart rate wise the watch has been 100% accurate. I've tested MY WATCH against other monitors and they ALL MATCHED.
As far as calories. The watch calorie count differs greatly from the treadmills at the gym - by far. But it's my contention that the treill readings are bogus and tend to trust the watch