A 2x4 stud wall is the wat to go. Furring strips directly on the foundation only saves a few inches - lets be reasonable here. Leaving a 1" gap between the foundation and the 2x4 plus th3 3-1/2" width of a 2x4 is 4.5 inches. A 1x strip is .75", save a huge 3.75 inches (7.5 for 2 walls). Unless you have a small basement, you won't notice that loss! A 12 x 12 room becomes 11.7 x 11.7.
There is the danger that the wood will act like a wick and draw moisture thru the foundation. I can't answer this either way.
The biggest drawback to furring strips is the fact that no foundation wall is flat. You won't notice the wavy wall until the rock is up and painted. Then it'll be too late.