Hi Melissa,
I grant GWF more accuracy because it is designed to measure caloric expenditure without using heart rate as part of the equation. Heart rate is only accurate when doing aerobic exercise; that's always been the caveat when doing heart rate training. Heart rate is only a proxy measure for caloric burn. It's simply a correlation that proves to be very strong when doing aerobic exercise, but is much weaker when doing anything else. Think of it this way: your heart rate increases substantially when you get angry, or stressed. But this does not mean you're burning more calories. To be burning more calories, your body has to be using more oxygen to operate more muscles. It's the increase in oxygen uptake that creates the increased caloric burn; not the increase in heart rate. What this means is that a heart rate monitor will pick up increases in heart rate and think you're burning more calories, even though your oxygen uptake has not increased. Hence, it over estimates your caloric burn when doing daily activity, or when weight training. Weight training, especially legs, can shoot that heart rate right up. But unfortunately, traditional weight training does not increase oxygen uptake to a corresponding degree. Hence, an over-inflation of calories burned.
Another problem with the heart rate figure is that, unless you've done the physical tests to determine your personal maximum heart rate, the monitor is going to base your exertion levels (and hence, calculate your calorie burn) on a formula designed for the general population. If your HRMax is higher or lower than the population average, then the monitor will classify you as either working extra hard, or not hard enough. Your calorie burn will reflect the intensity that the monitor calculates. Ergo, there's a built-in level of inaccuracy when measuring caloric burn via heart rate monitors.
Does all this mean that the GWF is more accurate? According to the research they cite, it's accurate to within 10% for daily living activities, and 5% for exercise. I can live with that. The GWF uses 4 measures that it computes in an algorithm to determine caloric burn. None of those measures are the heart rate. They're measures that have proven more accurate in all activities, not just when doing aerobic activity. Hence, if you want to know a good approximation of how many calories you burn, all the time, a device like GWF is what you need. If you just want to know what you burn during an aerobic exercise session, and are interested in developing CV health by training in heart rate zones for various amounts of time, then you need a HR monitor.
Also keep in mind that you have different HRmax figures, based on what exercise you're doing. So, you can't compare your spinning HR figures to running, to swimming, etc. If you want to know more about that, check out the book by Edmund Burke (ed) (1998) called "Precision Heart Rate Training" published by Human Kinetics.
Is all that as clear as mud?

. Years ago, Cathe wrote an article about how lower body resistance training could not be considered a cardio workout, even though your heart rate increases substantially during the workout. It was posted on the old website, but I don't see any of those articles anymore. Perhaps a dig through archived websites would pull it up? Or a search. Unfortunately, I have no idea what keyword would pull up the article. It was a long time ago.
HTH!
Sandra