Granted, I'm no expert on any of this, but it seems to me that heartrate only tells part of the story. Wattage, along with heartrate, would tell a fuller story.
Just because you're riding a lighter bike doesn't mean you're using less energy/strength. Doesn't it depend on what gear you're using--assuming you're on a relatively flat road?
It takes less energy to ride a lighter bike than a heavier bike at the same speed but that doesn't prevent you from working harder on the lighter bike. Just up your speed, lower year gear and/or increase your cadence. By the same token, riding a heavy bike does not--in itself--guarantee a tougher workout or one that uses significantly more strength. You still have to push yourself.

