Road bike raises my heart rate more tahn my MTB?
Heart rate is not an indicator of effort - its an indicator of fitness.

The best tool for measuring effort is a power meter, but they're not cheap.  Everything else is an estimate of power, rather than a measurement.

Your heart rate and your breathing rates will rise as your muscles demand more oxygen.

Could be your cadence is higher on the road bike and you're spinning, where-as you're mashing on the MTB which leads to different muscle fibres being used.