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The (...) statement of mechanics contained in Newton's equations or the (...) statement embodied in Hamilton's Principle (...) have been shown to be entirely equivalent. Hence, no distinction exists between these viewpoints (...). But from a philosophical standpoint, we can make a distinction. In the Newtonian formulation, a certain force on a body produces a definite motion - that is, we aways associate a definite effect with a certain cause. According to Hamilton's Principle, however, the motion of a body results from the attempt of nature to achieve a certain purpose, namely, to minimize the time integral of the difference between the kinetic and potencial energies. The operational solving of problems in mechanics does not depend on adopting one or the other of these views. But historically such considerations have had a profound influence on the development of dynamics.
[Classical Dynamics of Particles and Systems, S.T. Thornton & J.B. Marion, pg. 258]