Stronger X and Y axis ? which one

For the Y-axis it really doesn't matter. The key here is to make sure the linear rail bearing you select is appropriate to the direction of force being applied. If I were using the on-the-side method I would probably move the bearing up as high as possible to reduce the vertical length of the gantry arms thus reducing sway in the gantry frame.

for the X-axis while again it comes down to the type of rail bearing being used the key difference here is the distance between the upper and lower bearings and the rigidity of the member they are attached to. The lower photo of the top-bottom method not only has a significant spacing between the two rails, they are also attached to a member with substantial torsional stiffness. The machine in the upper photo not only has a fairly narrow spacing between the rails it also has a fairly long lever arm down to the tip of the router which will result in greater forces being applied to the rails and rail supports. The rail supports are also of limited strength and stiffness which will in turn result in lateral deflection of the cutter head which will affect cut quality. But if you were to put apples to apples using similar spacing and similar rail rigidity it really doesn't matter strength wise whether the rails are top/bottom or facing outward. The key issue here is the design of the bearing based on which way the load should be applied.