Does the elliptical ask for (and do you enter) your sex, age, height, and weight at the beginning of the workout? And, does it capture HR throughout the workout? If not, then its calorie algorithm is mostly a guess. If it is gathering all of these metrics, then it should be close to the other tools (unless it has a very crappy algorithm).I use a TICRX HRM paired with the Polar App when I run or use my elliptical. I also wear my Apple Watch. When I do a 10 minute Elliptical the Apple Watch may give me 60-70 active calories burned and the Polar App using the HRM will show 110-120. The Elliptical Machine will show like 180, lol. I use the Polar APP measurement and take about 10% off. I Have found the HRM with the Polar App to be spot on with the Hear Rate to net calories burned formula.
When I run the Apple Watch is much closer to the TICRX HRM than the elliptical measurement. I don't know why but it just is.