The small wheel folding bikes such as the Bike Friday and Dahon. These have 20 inch or smaller wheels, long seatposts and stems, and fold in half into a fairly small package. Assume they are very quick to fold and transport. Seem ideal for trips using several methods of transportation such as buses, planes, cars. These are sort of easy to transport. Might make good commuting bikes in large cities where part of the commute is bus and bike. Bike to the bus stop, ride the bus with the bike folded inside, then ride bike to work. Do it twice a day.
The other category of folding bikes are the ones that come apart such as the Ritchey BreakAway and Co-Motion Americano with couplers. These are 700C wheels and the frame divides into two pieces. They do not pack as small as the above folding bikes. And the packing takes longer. Not something you would do once or twice a day. Or even once or twice a week. But you have a normal looking bike when assembled. Seem ideal for someone who flies to a 1-2 month tour couple times a year. Should be cheaper to fly your bike.