I give an attempt of intuitive explanation.
I neglect any form of friction.
We can prove that, using kinetic energy theorem, that it will remain the same for two points. Therefore the speed difference should come from the fact that we have balls and not points.
Thus, the rotational effects must be considered. From a kinetic viewpoint, the ball advances to the right because all the points on the top right of the ball drive the ball to the right in addition to its gravity center's inertia. Besides, in addition to the latter, the rotational inertia adds.
An intuitive idea of a ball's rotational inertia is the following: each dot of the ball, except its center, pushes its immediate neighbor to the direction orthogonal to the rotation axis according to the three fingers' rule. Each point is thus pushed, killing more equilibrium and enhancing the adequate movement. It turns out that the effect comes from the fact that each point has a mass.
When the ball goes down, rotation inertia is increased because of the gravity exercised to each point of the ball, increasing rotational inertia of the ball, which gains speed. When the ball goes up, rotational inertia decreases but the cycloid is done such that the ball has an overall increased rotational inertia.
Specifically, in case of no friction, the ball has a rotational inertia higher when it goes up than if the trajectory was a line.
Note that, in presence of friction, this explanation is rejected but I give it to you as an exercise.
EDIT : I leave the comment originally as it was to point out a mistake I said. The kinetic energy theorem is not needed and the statement I wrote about it is wrong. So ignore it.