Aitor,the result of the experiment can show a longer distance for the spring or a longer distance for the string.
I do not understand why you keep revering to relative distances, especially since the distance force is being applied to the brick in you experiment is the same whether or not it is being pulled by the string or via the spring. Can you see from this force over distance plot that the force applied with the spring is different than it is with the spring although the distance those forces are applied is the same as the dropping distance of the lead mass in Lasse's experiment with a 2.4 N/m spring?
Remember time is running from right to left in this plot, so the break in the slope of spring force marks the point where the lead mass hit the ground and thus the acceleration on that end of the spring went to zero. The deflection of the spring was around .12 m when the lead mass hit the ground in that simulation, a distance that would be easy to see in a video.
Since the area under the green curve for the spring is larger than the red area for the string, the work energy applied to the brick will be larger with the spring and thus it will produce a larger launch velocity.
I think you need to focus on the relative launch velocities, not the relative distance the brick has traveled when the lead mass hits the ground. Why do you think the relative distance at the point the lead mass hits the ground is important? Is it because that is something you can see in comparative videos?
What I would suggest is that you measure the velocity of the brick as it passes a point that is equal to the dropping distance of the lead mass from its zero velocity starting point. Tom's timing lights would be a neat way to do it, but you could also use Tracker to analyze a high speed video as Alejandro is very adept at using it for velocity analysis.
As Lasse did you could also measure where the brick hits the floor to get an ideal of which case had the higher velocity. In that case I would make the edge of the table close to that .56 m launch point so that friction losses would not have any time to reduce the launch velocity.
If the impact distance of the brick hitting the floor is what you are referring to, then that would required a bit more analysis in the model to calculate the impact distance expected for a fixed height and different horizontal launch velocities. From an experimental standpoint, the impact distance would make for a simple comparison of the relative launch velocities, so if that is what you are referring when you are talking about longer distances then you are making perfect sense.