Normally there are about 0.125% rate difference.

But cash purchase will help you to get the property. And you have more time to shop around the rates. If you plan to get a purchase loan, technically, you can get the best rate on the market for the closing period(let's say 30 days). But for refi, you can wait for the best rate. But sometimes, when the rate went up(like the past 3 months), then the earlier the better.