Newton-type methods are fundamental techniques for solving optimization problems. However, it is often not fully appreciated that these methods can produce significantly different behavior when applied to two equivalent systems. In this paper, we investigate differences in local and global behavior of Newton-type methods when applied to the first-order optimality conditions for the logarithmic barrier formulation of the linear programming problem, and when applied to the perturbed first-order optimality conditions for the linear programming problem. Through theoretical analysis and numerical results, we show that Newton-type methods perform more effectively on the latter system than on the former system.