Since computations at strong coupling are hard, if not impossible, to do, any method that can provide a handle on strong coupling computations is great. In that sense, both lattice and AdS-CFT are good. To be honest, I don't even think one should be comparing the two methods. I shall however try. Fermion doubling is an issue on the lattice (I am no expert and am sure that there are ways to get around it) but that is not an issue in the AdS-CFT correspondence. The AdS-CFT (more generally, the gauge-gravity) correspondence gets weaker as the supersymmetry is reduced and things can get dicey, I believe, when there is no supersymmetry. Lattice methods might work better in such situations (think of pure QCD).