woofer combo & alignments: on large vs few small

The Multiple/small configuration can be as applicable as a single large.One large:pros 20Hz bass,cons- have to do with settling time and speed as frequency increases.Small/multiple:impedance usually isn't an issue,multiples can have similiar radiating area,lower distortion (each driver has less excursion),faster recovery time,smaller box (relatively speaking),better in-room distribution of bass.Con:usually don't go sub 20Hz the way a 15-18-24" can.
Never been a big fan of side-firing.Integration/phasing is more complex and sometimes leads to unusual bass nodes-depending on room characteristics.Just another $.02.-MO.

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")

The bigger woofer does not have to move as far, but has a harder time moving at the same time, the smaller woofer has an easier time moving as a unit but a harder time maintaining this as it has a longer distance to travel. The enormous research into cone material of the last 30 odd years have been directed toward this problem of cone linearity. The classic distinction was smaller woofers were faster while bigger ones went deeper. This has been greatly blurred in modern designs. Theory aside, you can get good results going either way. I would focus on the sound of the particular speaker as a whole, not the size of its drivers. The virtue of the side firing driver is in great debate, as was pointed out above they increase the problems of integrating the sound in your room.

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

When woofers are at play,the smaller goes to and fro while the larger over-shoots the mark.In packs,there is safety in numbers;>