Ask your own lender first
Lenders routinely charge existing customers more than they charge new ones for the same loan. The ACCC's home loan inquiry found borrowers with loans three to five years old paying on average 0.58% more than new customers, and loans over ten years old about 1.04% more. A phone call that says "I've been offered this rate elsewhere, can you match it?" costs nothing, and if it works there are no switching costs at all. Put the rate they offer into the new-rate box and set the costs to zero.
What switching costs
For a variable loan the costs are usually modest: a discharge fee from the old lender, state government fees to register the discharge and the new mortgage, and sometimes an application or valuation fee. Exit fees on home loans taken out after 1 July 2011 were banned, but discharge fees are still allowed.
Two costs can change the answer completely. Break costs on a fixed loan depend on where rates have moved since you fixed. When rates have gone up since you fixed, they're often small or nothing, which is worth knowing right now. Lenders mortgage insurance can apply again if you owe more than 80% of what the property is worth.
The trap in the lower repayment
The saving shows up as a lower repayment, and a lower repayment is easy to spend. The green box shows what happens if you keep paying what you pay now. That's usually where the real money is.