I have a Surly Long Haul Trucker and a Bike Friday New World Tourist that was built using measurements from the Surly LHT. With that said, there are a lot of differences between the two bikes, despite using the same measurements to create the same fit (riding position) between them.

My views are based on my own personal riding experiences, so others' views may be different. Compared to the Surly LHT, the BF NWT is:
-More agile. Way easier to dodge around obstacles and squeeze through tight spaces.
-Able to accelerate faster. A roadie that I passed told me that I should remove my rear safety triangle because I was going so fast.
-Less stable. The full-size touring bike tracks straight. The 20" wheel bike's zippy-ness means that I can easily ride no-handed on the Surly, and not so easily on the Bike Friday
-Less comfortable when going through potholes, gravel, cobblestoned roads, etc. It's a given with a smaller wheel size and narrower tires.

This is comparing them when unloaded. I have yet to do a loaded tour on my Bike Friday, but here's to hoping that it will be more stable than I am expecting it to be. Basically, I'd take the Bike Friday if I had to go through an obstacle course or a sprint, and the Surly if I had to do a longer ride through rougher terrain. I alternate between them. When I get bored of riding one, I switch over to the other one since they ride so differently.