Which sounds better 2 way or 3 way speaker design

When you start with a fallacy as your premise, you shouldn't be surprised at the questionable validity of your conclusion.

Perfectly legitimate question to me ...

Three way speakers with concentric mid/tweeter designs are another twist that offer very good results. 

6 of one. The square root of 36 of the other.

There can be number of variables approaching infinity related to speaker parameters and considerations. I’m with @skiznfliz on this one: put them in your room and listen to them.

To say, as the OP does, that "a 3 way design will give the listener a much better chance to hear the full audio spectrum as opposed to a 2 way design" is like saying a car with five speeds must go faster than one with only four. It reflects no understanding of what drivers in a speaker actually do.