Road bike brakes

These are just entry level Shimanos, so I know that probably makes a difference.  But, would it make that big of a difference? 

The brake pads are very close to the rims, so I don't think that's the problem.  I'll check the centering of the calipers on the posts.

It does make a difference.  And brake pad compound (like tires) makes a big difference as well.  A lot of people will "upgrade" 105 and Ultegra brakes with Dura Ace pad inserts as they seem to brake a little better.

It also depends on the cable and housing for the brakes as well.  If the brake housing is long and/or very flexible it can cause the brakes to be "spongy" and the stopping power will diminish.  Think of how race car teams use braided steel brake lines in place of the factory rubber ones.  Same concept .....

There will always be a big perceived difference when you go from MTB brakes to any road brakes.

I agree.  I think it would be fairly difficult to "endo" a road bike with the front brake, but it is easy on a MTB.     Also braking from the hoods, you can't get as much hand leverage as you can on a flat bar lever.  You will never have the same brake feeling as you do on the MTB.  

Make sure you have newer, clean pads that are aligned right.  The pads might not be worn, but if they are a little old, the rubber can harden.   Also make sure the tension is correct on the brakes.   You should be starting to apply pressure on the rim when the brake lever is less than half way pulled.  Full pressure should not require pulling the lever all the way to the handlebar.  

With MTBs, you have to account for very severe braking conditions, but more importantly, precise braking control. Picking your way down steep, rocky or rooted single track requires precise brake modulation. You just don't get that with the small caliper arms on road brakes. Also, on the road, you brake an awful lot less, making braking relatively more important in the dirt.