A larger down payment reduces your loan-to-value ratio, which typically earns you a lower base rate. Points reduce your rate further from that base. The question is: would you rather put more money down or spend that same money on points? The answer depends on your LTV tier and how long you plan to stay.
How LTV Affects Rates
Lenders price rates based on LTV tiers. Putting 20% down (80% LTV) gets a better rate than 10% down (90% LTV). The rate difference between 80% LTV and 90% LTV can be 0.25% to 0.5%. That is the same reduction you would get from 1-2 discount points. So a larger down payment might give you a rate improvement for free that you would otherwise pay for with points.
Direct Comparison
On a $400K home: 10% down ($40K) at 7.25% on $360K loan. Adding one point ($3,600) reduces rate to 7%, saving about $54/month. Break-even: 67 months. Putting 20% down ($80K) at 6.75% on $320K loan. You save an extra $40K in loan reduction plus about $120/month in rate savings vs the 10% down scenario. The larger down gives you both a lower rate and a smaller loan.
When Each Wins
A larger down payment wins when: you have the cash available, you want a lower payment, and you want to eliminate PMI. Points win when: you cannot reach a lower LTV tier, you plan to stay long-term, and you want to keep more cash in reserve. For first-time buyers who cannot hit 20% down, points may be the more practical way to lower their rate.