I own a HRM that I use during most of my rides and I noticed that I manage to push myself to the limit when I ride my road bike but not with my MTB. My max HR is always higher with my road bike, my average HR likewise. Is there an explanation for this?
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.