Speaker driver sizes - pros and cons

Here are typical differences. These are not cast in stone.
Advantage of small driver:
better frequency extension in the treble region
smoother midrange response
tighter focus in imaging & soundstage
Easier to use in any size room (smaller)

Advantages of larger driver:
Moves more air for more impact in midrange and bottom frequencies, large rich images.
Better excursion limits for better power handling
Normally produces large rich soundstage
Normally higher sensitivity

Disadvantages of small driver:
Less power handling
Cannot portray the large orchestral experience as well
Limited Frequency response in bass
Normally less sensitivity

Disadvantages of larger driver:
Normally not near the treble frequency extension
Normally not as clean in the midrange
Normally requires a much larger cabinet
Beaming is often a problem

@br3098 
Hi br3098.... I didn't forget to mention that at all.... I don't believe it.  I've heard 15 inch woofers that are very fast and dynamic.  Mass vs Motor tell the story.  As long as you have enough motor structure to push the mass speed is not an issue.  The problem lies when you start having too much motor. Yet another subject. 

@br3098 
In general, you are correct that a smaller driver is normally faster than a larger, but as I stated, A Properly designed driver: 
Mass is not always an issue,  understand that adding mass increases qms/qts,  adding mass decreases sensitivity... If you add a softer material, you'll find a more rolled off frequency,  if you add a hard material, you'll find extended frequency response,  The material added matters as well as if you coat the entire cone or add to the dust cap or even the rear of the cone.  
I'm really not stating an opinion. I've proven many times that a properly designed larger driver can be as fast as a smaller driver. 
I'm not sure what you mean by "over-driving a cone"  but proper cone, voice coil, excursion limits and even dust cap can produce a larger driver that extends well into the midrange, no doubt, depending on the final speaker design, you can certainly have beaming or lobing effects. but I have built and know where a set of speakers are right now that are a 15 inch 2 way that do a great job,  all drivers are custom modified for a natural rolloff at 1800 hz and when set up correctly,  they are excellent. 
Your overall premise that a smaller cone extends frequency smoother than a larger cone is correct.