what benefits does a road bike give over a regular mountain bike for casual cycling?
I think a road bike gives you better efficiency so you can go further with less energy and do it quicker. This is because they are:


Lighter - Less mass to get up to speed and keep moving.
More rigid - less flex, so the bike itself absorbs less pedal energy, meaning when you pedal, more of that energy is used to propel you forwards.
Less suspension, as suspension on a mountain bike works by moving oil/air around, and that warms up - you're providing the energy to warm the suspension up instead of moving forwards.
Have higher gears, so you can go further for one revolution of the pedals.
Have thinner tires - For less contact and friction with the road that would slow you down.
Have higher pressure tires - So they squish less and don't use up energy.
Get you in a more aerodynamic position so you incur less wind resistance. But, this might mean you feel less comfortable.


You might get:


Fun from choosing one and getting bling'ed up with a new shiny bike you can show off and take pride in.
The buzz/addiction for cycling more and wanting to go on longer rides.
The ability to keep up with other road cyclists who you can be buddies with, especially if you join a cycling club.
Fitter because you cycle more so you live longer.
A strange desire to wear lycra which will show off your body better and may attract the opposite sex, and you might end up with a better sex life.