A higher down payment will help all the way around, from reducing your monthly payment to eliminating your PMI, and lowering your interest payments over the long run if you plan to stay in your home for many years.
The question becomes, how long will you live in your home for the return on your investment to pay off? and do you want to keep some liquidity for unexpected expenses.
Putting down a greater down payment certainly makes your offer stronger and reduces your total interest payment. Your monthly payment will certainly go down, however, how significant that you will have to judge yourself. You can yuse the mortgage calculator and check out different scenarios.
Use this calculator: http://www.mortgagecalculator.org/ and you'll be able to try several down payment scenarios and choose which is best for you!
Good Luck becoming a home owner!