I think the examples may help........

A $100,000 loan at 4% over 30 years = 360 payments of $477 and total interest of $71,000. Paying $550 instead = 278 payments and $53,000 paid in interest. A $100,000 at 3% over 30 years is payments of 421 for 360 payments with a total paid $151,000 and interest paid of $51,700. So yes if you only compare the interest paid paying more saves almost the same amount over the life of the loan as paying a lower rate. Now that doesn't account for inflation $550 today will buy you more then $421 will in 23 years. OR how it will lower the interest paid if you keep the payment amount the same. But, it also doesn't include closing costs.