Well, larger woofers generally have more bass extension/output, since physics dictates that one needs to move more air to get more bass.
The trade-off is that in general, the larger a driver unit is (a woofer/midwoofer in this case), the heavier it is, which means it has poorer high-frequency response. Since bookshelf speakers are more-or-less size-restricted, woofer calibre usually doesn't go above 8 inches. Floor-standing speakers have less size restrictions, which is where one begins to see 10/12/15 inch woofers.
Of course, given the high-frequency response issue, woofers that large all but require a dedicated midrange driver, which creates a three-way (or more) speaker system. That's where one gets into the whole enclosure and crossover science. Deep magic indeed...