Wind, cold, wet roads, position, clothing, comfort - all can affect the power required to maintain the same speed.
Hydration, sleep, caffeine, illness, position, comfort, effort - all can affect the HR needed to maintain the same power.
If you did the same route, on consecutive days, with similar clothing and weather conditions, you might be able to remove a large number of confounding variables, but if you want to know if the road bike is faster for the same power, you need a power meter (ideal pedal based so you could switch the same power meter across bikes).
One potential reason for your HR being the same on the road bike could be that your upper body/core is working harder to maintain position, while your legs are working less hard. I think we need more data!