Have done a few A/B tests between my road bike and my commuter hybrid (including front-mount child seat and Marathon Plus tyres!), and I found I can generally go just as fast on my hybrid, but it takes more energy so it's not as sustainable. I guess this might be to do with air resistance, i.e. in any given conditions there is a limit to how fast I can go, and the road bike lets me go at that speed more efficiently. And possibly the tyres, but I think the difference in speed between tyres is overrated, lots of times I've matched road bike speeds on my hybrid and it never FEELS as fast, so perception is a big part of this.
The road bike is a Cannondale Optimo with low handlebars, and I actually find it easier on my back then the hybrid when trying to go fast, maybe because I keep trying to lean forward on it, although the hybrid is more comfortable at a slower cruising speed, i.e. canal towpaths.
I avoided drop bars for a long time but very glad I chose them for leisure/fitness cycling. For commuting and family rides I'm not really fussed either way, there is minimal difference between them on a 5 mile commute, although the road bike is more fun.