15 lb is a huge difference.

On the flat, the light bike will accelerate faster and with less effort (from a stop, or speeding up while on the move) and will be easily flicked from side to side (e.g. to avoid a pothole) and unweighted/hopped (e.g. if going over that pothole). Climbing hills, its hard to imagine anyone who wouldn't notice hauling the weight of two gallon jugs full of water, and that is about how much weight we're talking.

Also very important: the type and quality of bike that is 18-20 lbs versus the type and quality that is 34 lb. Unless the 34 lb bike is a 20 lb bike weighed down with 14 lb of stuff, which raises other issues!