In asking this question, you run into the real issue, which isn’t “price.” Our word “cheaper” has two meanings: of lesser quality and at a lower price. However, usually, the two are tied together: a lesser price often means getting lesser quality.
However, the terms “quality” and “price” can mean many things. Quality can mean better ingredients, a better recipe, faster delivery, more features, etc. Price also has many different dimensions: the initial price paid in money, the cost in time and energy, the risk in buying, the cost of ownership over time.
The point, all competitive comparisons are specific: based on the unique needs/preferences of a buyer and the selection of alternatives in the marketplace. The most generic comparison, a dollar price, is meaningful, for example, always depends on the resources of the buyer. If you are a billionaire, prices differences mean less to you than someone struggling from paycheck to paycheck.
In some situations, you can certainly succeed offering a lower price in one dimension or another. Buying the same can of chili from two different stores that are equally convenient, reduces the comparison to price paid.
However, in many situations, lower prices are meaningless. If you need an medical operation, does a difference in price determine which doctor you choose when you can afford to pay any difference between alternative doctors? No. Nor should it.
All strategic decisions require thinking about the issue holistically, but we need aids to simplify that process. This is why various concepts like the five aspect of a competitive position were developed in the science of strategy.