I'd not trust any of them- all seem to over estimate, the HRM will normally say less then the gym machines but none are really reliable as they assume your fit, healthy, properly hydrated and working at your peak, they do not allow for days where your fighting infections (practicly everyday as many infections fall under the radar) they do not account for us getting better at the exercise we do: If I run 1 mile for the first time, I 'shock' my body, it burns x calories. But if I do this same 1 mile run every day, eventually I get used to it, my body learns to become effiecient and burn fewer calories, the HRM changes and reports a lower heart rate but the difference in calories burnt is minimal, and if I keep doing this for good, eventually my body relies on me doing it and has managed to burn far fewer calories then any machine or HRM tells me. Disappointing but the sad truth.
The best thing you can do is to keep chopping and changing your programme, keep yourself interested in what you do and do not rely on your exercise programme to burn any calories, use it as a back up by all means and it has tonnes of additional benefits but in terms of loseing weight, most of it comes from what you eat.