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When feed and page prices differ, which should win?
The one your checkout charges. Both published sources should equal it, and if they cannot, the feed should be the one you correct, because it is the one an agent trusts without loading a page.
Why it happens
Agents read whichever source they reached first and treat it as authoritative. There is no reconciliation step, because from outside there is no way to know which of two published numbers is correct.
A quoted price that does not survive to the cart is a specific kind of damage. It reads to the shopper as a bait price, and it teaches the assistant that your quotes are unreliable, which is a harder thing to undo than a missing field.
This comes up at the Compare stage. The full treatment, including how to reproduce it and what to change, is on Feed price and storefront price disagree.
Related questions
Run a free scan and find out which of these your store actually hits.