As Thorn said, the weight difference will be noticeable mostly in climbing and acceleration. Since you live in the flats, your difference will be in how quckly you can accelerate your bike. A racer would refer to that as "jump", how quickly you can accelerate into a sprint. Or how soon you can reach full speed from a stop. How responsive the bike feels to your immediate input. And most of what you feel in acceleration is from the bike's "turning weight", the weight on the rims and tires.

Backpackers rightfully place alot of emphasis on pack weight, but that weight is carried on the person's body, straining shoulders and backs and stressing knees when hiking downhill. Plus, every step results in a bit of up and down movement, so the weight is lifted a couple inches with each step, even on the level. With a bike, the weight is carried on the wheels, and the weight gets lifted only on an uphill.