Here's the 50,000 ft. overview:
Advantages:
Assuming all other things are equal bigger speakers can play louder, more efficiently, and can usually produce lower sounds.
Disadvantage:
You need a larger enclosure as compared with smaller speakers.
And here are the technical reasons why this is true:
The biggest benefit to using a larger speaker is sound pressure level (SPL). The more piston area you use, the higher SPL and power handling potential you have. Larger speakers couple better acoustically to the interior of a car and give a more impressive impact than a smaller one.
Knowing this, people often get confused when considering multiple small speakers Vs. fewer larger ones. Often, a single larger driver would be cheaper than several multiples, may consume less valuable trunk space, cost less or fit the person's needs better than another driver. Also, larger drivers usually have larger voice coils and larger magnet structures and thus will handle more power than a smaller driver.
The big advantage of multiple speakers is that the power will be distributed to different voice coils - reducing the likelihood of power compression at typical listening levels. Power compression is a loss of amplifier power and change in speaker parameters due to a rise in the DC resistance of the voice coil as a result of heat. Multiple speakers are less likely to suffer from this effect and will generally sound cleaner at higher output levels.
As far as actual reproduction, it really isn't fair to say that a smaller speaker will perform as well as a larger one in every vehicle due to the transfer function of the vehicle. If you were to use a two comparbly sized speakers, each with different -3dB points, say 20 hz apart you are definitely going to notice a difference in the way both systems sound even in the audible (or shall I say "useable" region).
In larger cabins, larger speakers will have a distinct advantage in that they will couple better with their environment and give a more realistic performance than will a smaller driver.
The 8" home speaker you heard probably sounded big because it was in a large enclosure tuned for bass with a bandpass enclosure and the room you listened to it in was a good environment. Home audio is different like that. Seats, carpet, glass, and plastic coupled with tight install space requirements, power capabilities and enclosure size restraints are common car audio challenges and in this world bigger tends to be better in terms of moving air.
But most of all, bigger speakers stroke the egos of millions of bassheads all around the world simply because they're cool! 8)