Can I expend same or less effort riding a mountain bike than road bike? I know nothing about engineering.

I feel like I can expend the same or even less effort riding a mountain amd a road bike (if going slowly) but feeling is not reliable, so I hope to get some insight on this matter.

Let's assume the mountain bike has a hard fork, hard tail, really thin tires.
At same price as the road bike. The two bikes are going for the same distance on a smooth road, with no wind. I don't know if climbing and decending make much difference.


What I guess is, if I am going slow, so the aerodynamics of a road bike will not make much difference, won't I using almost same effort to cover the same distance?
Gear ratios affect fuel consumption, so can I manage my gear ratio and speed to save total work I expend? Will a mountain bike will require less work to cover the same distance? 
When riding in the city where you have to frequently stop and start, does a road bike need more effort than mountain bike since it has higher ratio gearing?
Is there some way to test this without a lab environment? I can't find a way to measure how much work I'm doing, and total work I expended. 


Please feel free to educate me, I just want to know more.

Where I got this weird idea was from my wife:

She got a hard tail hard fork DIY XC bike, with carbon frame and fork. it was decently light, at about 10KG, slick tire with high pressure and very narrow. It cost bit more than US$1600.

But, she only rides it if we are going out town. She commutes with a US$45 lady bike, she said it was not much difference riding this bike, if under 4km.

I tried her lady bike, it was pretty easy riding short distance in the city, but very hard at longer distance on account of riding posture, and very small bike -- riding slowly of course.
Whelp, how to answer this? Depends what you mean by 'less effort' I guess.

I'll give the short answer up front. Road bikes are more efficient (therefore less effort to ride) than mountain bikes on road surfaces. We know this because road bikes have been optimized for speed and efficiency for a couple of hundred years. Geometry mess, riding position, wheel size, tire width and gear ratios all contribute to this. 

To address points 2 and 3 about gearing. Everybody has pedaling cadence and gear ratio that is most efficient for them. A casual rider would use a lower gear ratio, a pro racer will use a much higher one. The availability of lower ratios does not make a bike more efficient (as long as they are low enough for the rider), Road bikes have enough gears to allow selection of an efficient ratio and their lowest ratios are sufficient to allow easy acceleration from a stop. Mountain bikes have lower ratios than road bikes to allow riding up steep inclines (and to pull their greater mass around).

Is there a way to test this? Yes. The advent of (relatively) affordable and accurate power meters make analysis of rider performance available to even casual riders.