Think high school physics. Force = Mass x Acceleration. When you're climbing a hill you're fighting hard to overcome gravity while air resistance and rolling resistance, which are important on the flats, are no longer significant. Rolling resistance comes from all the friction in the bike's bearings and tires on the road: better bearings and thinner tires with less surface on the road equals a faster bike. Mass is how much you and your bike weigh and force is being generated by your leg muscles. The ladies that passed you likely had more of a weight advantage than a bike advantage. The gearing provides a mechanical advantage but in the climbs you shouldn't have a gearing issue on your hybrid. How you drop gears as you climb can make a difference. Shoot for a constant cadence which is the RPM of your pedaling and drop gears to maintain a comfortable pace. My road bike has a lot more top end gearing which means I can go far faster on the flats and downhills which provides for the faster overall time in a ride but the gearing doesn't provide an advantage in the climbs. If you want to climb fast, weight loss is significant. The road bike will be lighter but as others have mentioned as much body mass as you can get rid of is important with the exception of those leg muscles which provide the force.
I would get a road bike because they're a lot of fun to ride but don't expect it to suddenly having you flying up the hills. When I purchased my road bike the shop owner told me "any bike you buy from my shop can be raced professionally, and if you lose, it won't be the bikes fault".
Johnny P
Be Self Propelled