Most of the common problems can be solved by all the softwares you mentioned. Any way it depends on your problem details.
As said by the others, it depends on your problem, especially, on your materials and loading phases. In any case, respect the fact that both Abaqus and Ansys are general purpose packages and obviously they failed to cover very deep problems in different engineering fields.
One of the main differences between ANSYS 12 and ANSYS 13 is that the former keeps both old and new generation finite elements, while in the latter the old generation is archivated. In this respect, I prefer ANSYS 12. I have never worked with ABAQUES, so I cannot tell about it.
Both ANSYS and ABAQUS are capable to solve PDE by using FEM. However it depends upon the governing equation as well as boundary conditions. I have used both software for fracture analysis. The new approach XFEM has been incorporated in latest version of ABAQUS. XFEM is quite efficient to solve discontinuous problem. Hence I will prefer ABAQUS.
Actually I want to calculate the modal analysis of cracked composite material...
I would go with ABAQUS, Its interface is easier to manipulate and it has the same general options available in ANSYS
If you are looking at working with cracked composite and fatigue analysis, I would also recommend ABAQUS, because of its XFEM capabilities. However, if you are attempting to solve problems of crack growth in areas with compressive residual stresses were the crack closes you will face issues with XFEM, because of the crack closure phenomenon...
As mentioned it depends on your problem details, but ABAQUS is more preferred due to its XFEM approach in fracture problems.
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