The brakes may simply need to be adjusted if you have to be in the drops to apply that much leverage to safely stop?
It really shouldn't take that much at all to effectively engage the brakes.
If they are Shimano, check to see if the quick-release is engaged?
As the others have noted it could just be a fit issue, because, while riding most of the resistance is coming from your wind profile and I have to think that your hybrid would place you in a much more upright riding position and therefore a larger wind profile. In theory, this should make it harder to achieve the same speed with your hybrid vs your road bike?
This is a place to start for assessing your current bike setup, it doesn't mean it's a panacea, but it has worked for many if you are interested. (Ignore that it specifies a particular saddle type)http://cobbcycling.com/cart/V-Flow_M...b_installation