Yeah, I think using the "language of power" is just confusing things here, because you have no idea what your wattage is, nor your heart rate, so it's just a waste of time talking about that. And really, your power output is your power output, and it doesn't matter the type of bicycle...or if it's even a real bicycle. So let's just stop talking about power like we know something, because we don't.

Let's just say you feel like your effort level is higher on the road bike. Now why would that be?

Assuming the usual differences between Road and MTB bikes, we know the Road bike has less drag and therefore rolls more efficiently for a given effort level, i.e. faster. The faster you go, though, the more wind resistance you need to overcome, which requires more effort. So, it could be that you're going faster, and worker harder, but that depends on how fast you're actually going.

The other thing we know is that Road bikes have taller gearing than MTBs, so if you're not riding that hard, it will feel like the MTB is easier to pedal, which is true. So, if you're used to low-ish speed, low effort riding, yes, a Road bike built for speed will take more effort because the gear ratios are higher.

Get a speedometer and watch the numbers, and let us know what you see. If you're really imto it, get a heartrate monitor and do the same. The other thing you can do is figure out which gear combo on each bike yields the same gear inches (count teeth on front chainring and rear cog, and plug into a calculator like Sheldon Brown's Bicycle Gear Calculator) and compare your effort level in the same gear.