Ellen, dramatic differences in tire width do produce a dramatic difference in speed. Most of the time we're discussing the difference between a 23 and a 25 mm tire in which case it's pretty neglible. The tire construction and inflation can make the difference with such a small variance, not the tire width.

However, if you are comparing a "fat tired" bike to a road bike with 23 or 25 tires, you will find that the narrow tires have significantly less rolling resistance and require less effort to maintain or achieve more speed. Depending on your terrain and your ride goals, you may want to look into recumbents. The position on the bike is more aero dynamic than the townie but recumbents, just like diamond frame bikes, have their pros and cons.