Getting someone to switch because you offer more of what they were looking for when they choose the one they have now is essentially impossible. For starters, they’re probably not looking for more. And beyond that, they’d need to admit that they were wrong for not choosing you in the first place.
So, you don’t get someone to switch because you’re cheaper than Walmart. You don’t get someone to switch because you serve bigger portions than the big-portion steakhouse down the street. You don’t get someone to switch because your hospital is more famous than the Mayo Clinic.
The chances that you can top a trusted provider on the very thing the provider is trusted for are slim indeed.
Instead, you gain converts by winning at something the existing provider didn’t think was so important.