I experience the same "problem". I discussed it with two exersice physiologists, and we came to the conclusion that it had to be related to number of muscle groups you are using on the trainer vs road.
We assumed that your heart rate relfects total body power output, from all muscle groups. We also assumed that the more you extert a specific muscle group, the more it hurts.
Looking at the trainer, it isolates many of your muscle groups, and concentrates the effort into your thighs, specifically the quads. So for a given power output (heart rate), you are going to hurt more and fatigue quicker because the load is being disproportionately carried. By contast on the road, you will utilise your hamstrings, calves, occasionally upper body as well as adjust positions, all of which push your heart rate up and spread out the total work load.