The scale is measured fretboard side of nut to bridge, but if you're doing some thinking about it for relativity's sake, then it might be easier to think of the scale length as nut to 12th fret x 2.
Ergonomics does impact where a "scale" fits on the size of a bass. Take for example, a34" scale bass with the upper horn reaching to the 16th fret, and the bridge located about six inches in from the body edge.
Compare that to a 35" scale bass with the upper horn reaching to the 10th fret, and the bridge located right on the edge of the body.
In this case, the 34" scale would feel much longer, as the headstock would be located quite a bit further to the left than the 35" scale bass. Where the nut/bridge/scale is in relation to the points where a strap is mounted, can really impact the feel of an instrument.
I know that some players also note that moving from 34" to 35" is really noticeable and requires an adjustment, I've never noticed, but then again, I play instruments of varying scale lengths pretty regularly so I'm quick to adapt. I prefer the feel of a med-scale length located a little deeper into the body...