Disclaimer: I don't own a Bike Friday, but I do have a sport bike with S&S couplers.
It takes me about an hour, even after some two dozen trips, to assemble or disassemble and pack the S&S bike. Part of that's due to size (I have to almost completely disassemble mine because of the large size; fork, bars, seat/post, derailer, and cranks -- shorter people don't have to take the cranks off). That doesn't include fenders or racks. Also, packing is tricky, because just the bike fills the case. I'd suggest going with 26" or 650B wheels, so you don't have to partially dismount 700C tires to get the front tire in and the case closed. The case is bulky, and would require some shipping (UPS or similar) from your departure to your arrival location.
As Fred notes, when it's together, it's as solid as any other bike, just about a half pound heavier. The only adjustments needed are seatpost height and handlebar tilt. It's a beauty.
The S&S premium seems to be $600, which is a lot on a Long Haul Trucker frame, but it's not as significant when you put it on a custom $2000-4000 frame.
I think the BF case is slightly smaller than the S&S case -- check out their web site for details. (I think the S&S case is 26"x26"x10" for comparison.) I'm intrigued by the BF idea of using the case as a trailer. Pack the trailer and your gear in a duffle, unpack the bike, stack the case on the wheels, dump duffle contents into case, and ride off. That's the advertising, but I'd like to hear from someone who does it to see if it's really that easy.