Most households already live in one store. If the family uses iPhones and iPads, Apple Books is the simple path. If the readers are on Kindle or Fire tablets, Amazon is usually easier to live with.
Still compare the price and the formatting, and check whether the book is free that day. The same title can show up in both stores at different prices. Tiny Kid Books lists both links when we have them, so you can choose without a second search.
Use a child profile or a supervised account where the store offers one, and keep purchase approval on. A complete children's book is a safer bet than a random bundle.
The logo on the app matters less than the habit. Look for stories your kids actually finish.