Generally a higher monthly payment is better than saving to make one large payment.
1) The faster you decrease the principle, the lower the amount of interest you will ultimately pay. If you owe 1,000, and have minimum monthly payments of $10 but decide to pay $100/month starting in January, in February you only owe interest on $900. Then in March you pay interest on only $800. By April you're paying interest on $700. On the other hand, if you keep paying just $10/month, in February interest is charged on $990, in March $980, in April $970, and so on. Get the balance down, as fast as you can.
That is the best reason to pay higher all along, but, if you need another:
2) A large lump-sum might create temptation to splurge in unintended ways in newer Mustachians.