woofer combo & alignments: on large vs few small

Actually it is simple, when a big woofer barks the many small woofers yelp and run away with their tails between their legs ;-)

What is the trade off in having one large woofer vs several small woofers?

A single large woofer is an easier load and can be put in a single box. Generally you get the most dynamic bass response (moves more air) and large voice coils cool better (less thermal compression which makes speakers sound dull at loud levels). They are expensive drivers and are limited in usuable upper frequency reponse before they start to beam.

Multiple woofers can achieve the same job as a large woofer provided you have many (similar surface area) and they are in separate cabinets (otherwise you'll inevitably get some increased backwave distortion). Smaller woofers will go higher in frequency before beaming/breakup occurs so they can have useable energy up well into the midrange. They will tend to be a more difficult load for the amplifier and small voice coils tend to have more trouble with heat dissipation (get hot and sound dull). Of course multiple woofers covering the same frequencies also leads to comb filtering in the bass if they are used much above about 500 Hz.

Some world class manufactors have moved from front firing woofers to side firing woofers. This seems to fit a wide room better but to me, this would can create cancellation and lack of coherence.

Side firing is fine as long as it is used only as a subwoofer. It will of course create significant problems if used above subwoofer frequencies. The principal advantage is in maintaining a narrow speaker profile at the front (a smaller baffle width helps to improve imaging in the upper midrange and treble where edge diffraction can make one aware of the speakers and reduce the effectiveness of the "disappearing act")