you can always change the gear range on MTB by going with a larger chainring.
since MTB can mean 26" or 29", 29" being the same thing as 700c, that and road has it's own smaller wheel variant of 650c, the gearing argument isn't valid.
for wheels, larger diameter = better rolling efficiency, so fatter slicks on 29'er/700c would give you even more rolling efficiency.
Lol, way to take a general question with a good general answer and give one example of a configuration that nobody would use as a counterpoint. Bet you're great fun at parties!
Generally mtb = 26 and rb = 700c. But wait, it could also mean a fixie or a single speed. Road bike could also mean a track bike. Oh it's all so confusing.
btw, fast roadbike tires are all about rolling resistance. A fatter tire has much higher rolling resistance so will slow you down. That's why running your tires at lower pressure slow you down (it's not, as you would argue, the slightly reduced radius)