I own and have ridden both a Bike Friday (Air Friday) and an S&S coupled steel bike on multi-day tours and event rides (Italian granfondi, French sportif and US centuries).
The Friday transforms more easily between its riding and collapsed states than the S&S bike, so is easier to stash in the trunk of a small car or take on board a train. The small wheels essentially give you a 20% lower gear in the same gear combination as a "full size" bike; conversely, it's a bit harder to get high gears on a Friday, though you can get a Shimano Capreo hub with a 9-tooth high gear (9-speed in stock form, but Bike Friday sells a version modified for 10 cogs).
On the flip side, all the folding parts make for a vaguer feel to the Friday. My first reaction after I haven't ridden it for a while is, "Do I have a flat tire?". And, of course, it can be harder to find tires and tubes (406 or 451 ETRTO size).
The S&S couplers are very secure and rigid. Their website even has a page of tests showing a coupled tube to be more resistant to twisting and bending than the same tube w/o the coupler.