A generalization of the diffusion-limited aggregation (DLA) model, originally proposed by Witten and Sander [Phys. Rev. B 27, 5686 (1983)], has been studied on a very large square lattice. This model has a sticking probability p for a random walker which is assumed to depend on the number of occupied nearest-neighbor sites in the cluster B, as p=α3−B. A dynamical phase transition between growth along the axes and growth along the diagonals is observed at a critical αc≊0.175. Our simulations also show that αc changes with the amount of noise reduction. Thus we show for the first time that noise reduction may change the asymptotic behavior of DLA models.