With the information you provide, the best answer that one can give is:
It depends.
It depends on support conditions, on load conditions. It may depend on matrix properties and reinforcements anisotropy and so on,
For example, the antisymetric laminate may have higher through thickness stresses at the edge because the Poisson effect in each outer ply are not the same and may be less stable in compression due the non-zero B and D matrices. However, under some load conditions, this may not be much of a problem.
And to be nitpicky, you are asking about laminates, not structures.
Best regards,
Laurent
2017-04-11 edit: edge stresses might actually higher in the symetric laminate could actually be worst since the higher Poisson's ratio is outside, producing a peel stress under tension.
Use the classical lamination theory to find ply stresses in the principal directions (longitudinal, transverse and shear). Use these ply stresses (or strains) in the desired failure criterion.
If you are interested in first ply failure, look at the safety factor you get for each ply. Be wary, some failure criterion are non-linear and your safety factors is thus also non-linear.
Otherwise, find the failure stress of the first failing ply and iteratively perform the analysis while killing (i.e. making all stiffnesses nul in their stiffness matrix) failed plies. repeat until last ply failure.
You can find the description of the process in Gibson's 'Principle of composite materials mechanics' among others. Be aware of the many underlying assumptions in the process though.