I did the same as you in late February and if you have the same experience as me, you will have great fun on your new bike.
What difference have I noticed?
Some people have mentioned riding position. I haven't noticed too much change there really, probably because my hybrid (it's the one in my avatar) is far more geared towards a road bike than trail or MTB. It has a high saddle position and I lean forward quite a bit. My road bike is a Giant Defy, which according to much of the stuff I read, has a more relaxed riding position. So, perhaps with different bikes I would have noticed more difference.
The road bike is certainly lighter, much more "tight", compact and responsive. It is also noticeably quicker, I average about 2 mph more than on my hybrid, which might not sound much, but the higher your average speed gets, the longer it takes to incrementally increase it, and I find myself moving along comfortably at speeds that I would have to work very hard to achieve on Hybrida. I have also noticed that riding into the wind isn't as hard work. I have found myself covering 7 or 8 miles further per ride on the road bike, but extra caution is needed to spot poor road surfaces sooner, I would rather take my chances with a pothole on a hybrid than a road bike.
One downside is that sometimes I find an ache in my thumb bones while holding the bars behind the hoods, but I hope that will subside as I get used to it.
Braking from the hoods was strange at first, and it is important that you get used to it. On my first ride, I actually went for where the brakes would have been on my hybrid, a couple of times, but of course they weren't there and I nearly came a cropper. I soon got used to that though and as the 3 people above have said in response to mjr's post, I would disagree that the brakes are weaker, mine are just as powerful.
I decided not to use cleats straightaway because all the advice I have had is that they take some getting used to, so rather than jumping in too deep I decided to get used to the bike first. Now I am used to the bike, that is my next move, and I will transfer the pedals to Hybrida as the old ones are getting a bit knackered.
A bit of a lengthy response, but hopefully has some useful pointers. I still ride the hybrid, it is a great bike and for commuting, and getting around town, it is super, but the road bike is a real treat. Good luck, hope you have as much fun as I am having.