eigs does not always converge, even if maximum number of iterations is significantly increased and/or solution tolerance decreased. Furthermore, it is random, i.e., non-repeatable, even on the exact same matrix unless random numbers are controlled to be the same at invocation.
eig is much more robust than eigs, and execution time of eigs is more unpredictable than eig, and can be longer. I've run nonlinear optimization algorithms in which eigenvalues (maybe the most extreme 1 or 2) appear in the objective function and/or constraints - even though the algorithm might start and finish (if it ever gets there) in a nice neighborhood in which eigs works just fine, the algorithm might have to go through some unseemly areas along the way, and eigs has a propensity for getting into trouble somewhere and muck everything up. I've rendered eigs to the ash heap of history after wasting too much time dealing with its nonsense. Someone should shoot it and put it out of the misery it causes.