This seems to make sense to me... basically, if you pull hard enough, you might actually involve what's past the fulcrum points, which would add to the overall "give" of a string. But I guess if you play with a medium or especially light touch, there's probably no appreciable difference.
The counter-intuitive part is ppal was saying the opposite... that the bass that was headless was spongier feeling, and by a very noticeable margin. This is what seemed odd to me and got my curiosity up.
Ahhh.... the plot thickens... I don't doubt for one minute you felt a difference, but based on what you just posted, I'm gonna' go out on a limb and say since you knew the strings weren't the exact same type, you probably mistakenly attributed the diff to the instrument instead of the strings, and the strings would be my first suspicion at this point.
Bottom line is, it really would be interesting to try both basses back to back with the exact same strings and then judge. I won't have this opportunity, but maybe someone else on the thread would.
No biggie, just noodling.