The basic idea behind both is the same except for the type of mechanism used to detect whether the buckling spring mechanism has been actuated. In the capacitive design, the spring pivots forward a hammer which forms a capacitor between two electrical contacts. In the membrane design, the hammer strikes a membrane similar to that of a normal rubber dome keyboard.
On paper, the underlying mechanism wont affect the user's experience. In reality, the two mechanisms require different hammers which in turn require different springs. The different springs have quite an impact on the tactility and noise of the keyboard. Most (if not all really) who have tried both will say that the capacitive design is superior in terms of tactile and auditory feedback. Problem is that they are harder to find, and the Model F PC/AT keyboard pictured in that link you posted is the only capacitive keyboard that can readily work with a modern PC. As pointed out above, the IBM/Lexmark/Unicomp Model Ms (except for the rubber dome variants) have membrane BS mechanisms.
I really need to start that keyswitch section in the IBM wiki...
