iPhone 14 Pro Max battery replacement: Authorized service vs local shop?

Hey everyone,
I’m planning to replace the battery on my iPhone 14 Pro Max and wanted to get some real-world opinions before deciding.
How big is the price difference between an authorized service center and a good local repair shop?
Is the quality noticeably better with authorized service (battery life, safety, etc.)?
Do local shops use genuine batteries or good alternatives?
Also, what about backup/data safety—any risks I should be aware of in either option?
Would really appreciate hearing your experiences and what you’d recommend. Thanks!