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
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