I've been using a SRM powermeter for several years and it allows you do the math with the least amount of assumptions. I weigh about 163 lbs and an easy ride will be about 35 kcal/mi. It's about 1/3 that of running but you ride about 3 times faster.
I've seen some crazy numbers regarding calories burned running. They translate into power outputs beyond what humans can do. A body can only do so much work as measured in watts which is power which is work/time. Suppose on the bike I can sustain 300W, I can't hop off the bike and run at 1200W. It's just not possible. I would be outputting around 300W while running as well and burning around the same number of calories.
That one would have to ride 3X longer time-wise to burn as many calories is incorrect. Unless you are riding at an effort 1/3 that at which you run at. A very, very, very rough estimate would be that you would have to ride 3X longer distance-wise.
I find that one does not burn more calories/time while running but due to the greater efficiency of riding, you just cover more distance in the same amount of time.
Using HR to calculate work is a very rough approximation. With a powermeter, you're already making one assumption and that is your efficiency. A powermeter only measures how much work you do, not how many calories your body used to do that work. A HRM that calculates calorie expenditure probably makes 2-3 more assumptions which renders the numbers basically useless.