The difference is HUGE! When you get on a set of skinny, hard, fast rolling, knob-less road tires, it will feel like your bicycle has been set free. The knobs on a low pressure mountain bike tire create and enormous amount of drag, when you no longer have to push against them the difference will be unbelievable.
You may also notice you are no longer riding with your chest stuck out like a sail. You will find the new, sleeker, aerodynamic profile allows you to maintain your speed with much less effort.
You will also notice the ride on the skinnier, harder, road bike tires is much rougher going over bumps and potholes. This drawback is well worth not having the drag. You may compromise by getting a fatter tire than allows for lower air pressure and gives you more cushion but I prefer the reduced drag hard and skinny tires give you.
You will probably notice the road bike is lighter and with your lighter bike and less tire drag it is much easier to accelerate on.
Going up steep hills you will probably notice the gearing on the road bike is higher and may miss the lower gearing unless you road bike is equipped with a touring gearing (3rd smaller inner ring).
You will probably not notice the lack of tread, even on gravel bike trails. For the most most part the tread is not necessary on gravel bike paths but if you corner hard in gravel you will notice that your wheels wash out much easier, so take extra care when cornering.
If it's a traditional road racing type setup, you will notice the handlebar and braking setup is different and that it's even a little harder to stop. At first you will also find shifting is a bit confusing and may take a little time to get used to.
You may also find your riding position is a little less natural and a little less comfortable.
Get a road/commuter specific bike. You wont regret it.