The depends of  the problem:

 a) SIMPLE algorithm is used more for steady-state problem

http://www.cfd-online.com/Wiki/SIMPLE_algorithm

b) PISO algorithm is more for unsteady analysis, depend of  your investigations, that is the case of unsteady partial cavitation problems.

http://openfoamwiki.net/index.php/PISO

In openFOAM there is PIMPLE, which is PISO and SIMPLE together. PIMPLE calls the algorithm depend of problem conditions.

Your issue is quite interesting. I have a couple of comments:

1) The shape of your mesh defines the directions in which perturbations propagate. This may explain why the wave is only seen in the XZ plane. For a 3-dimensional case of a sphere you should try to use a mesh that has the same aspect ratio in every direction. This means that the mesh in the sourroundings of the sphere should be at least axisymmetric (around the X axis).

2) In this kinds of simulations you have to be extremely careful with the effect of the box boundary on the solution. Whick BCs did you chose? I would check what happens to your solution if you:

a) Get the walls further away from your sphere.

b) Change the boundary conditions (e.g.: Wall (no-slip) to Atmosphere, inlet outlet, slip, etc..)

3) Maybe solutions for each time step are not completely converged, are you checking convergence (0 iterations in the piso loop for the tolerance you have chosen) in every time step? You can also try other solvers like pimple or pisoFoam. 

4) Flow around a sphere is a really complicated simulation, and taking 100% correct measurements of an experiment is rather impossible. I would recommend a simpler, academic case with documented experimental results.

1) There is no reason that at a single instant you see a symmetric pattern in an unsteady case. You should check for a long time interval.

2) Check the effects of the domain extension, you could have some outflow effects.

3) Always think about a chance of a bug in the setting.

Luis Francisco Barceló, thank you for your reply.

I used these BC:

Inlet: Velocity uniform fixed value, [0.01 0 0] m/s

Outlet: Pressure fixed value, 0

Walls of the domain: free-slip wall

Sphere: no-slip wall

Furthermore, I increased 20% of the domain size in all directions and the results did not change and I am checking the convergence in each time step.

Filippo Maria Denaro, thanks for your reply.

The flow does have a symmetric pattern during a long time interval, but I represented that with a picture because I couldn't manage to publish a gif or video :)

I suggest first to check the case of the steady flow at very small Re where the solution must be symmetrical in both plane.

As a matter of fact, the simulation was not wrong at all. I did some research and I realised that the flow is not symmetric to the XY plane, it does have an inclination angle. In addition to that, the lift coefficient is not equal to zero. Johnson and Patel found CL = -0.069.

Article Flow past a sphere up to a Reynolds number of 300

At present I cannot dowload the paper. I never analyzes such type of problem, so I can give you an opinion. It sounds strange that the time-averaged solution is not symmetric.