The Big Picture Story Bible
This storybook Bible is unique in that it doesn't break the bible down into individual stories (such as Daniel and the lion's den, David and Goliath, etc) but each chapter of the book covers many chapters (or even many books) of the Bible. The book as a whole does a great job of portraying the creation-fall-redemption narrative of the Bible. A major theme touched on throughout the book is God's people, God's place, God's rescuer and God's blessing, and how these themes played out through each time period of the Old and New Testament (and the fulfillment of all these things in Jesus). I appreciate that when appropriate, the stories in this book quote the Bible in a seamless manner.
Each page has just a few sentences, which makes it a great story bible for the youngest of kiddos who will sit down and listen to a book. We have been reading this book with Esther since she turned one (but, as the pages are paper and not cardboard, you will need to keep it out of reach of little hands!). However, it is not just a book for young kids. The concepts are still valid for older kids, and I think that children up to 7 or 8 would still enjoy this book, especially to help them understand the larger narrative of the Bible.
This bible comes with a CD but we have never listened to it (probably because right now we don't have a working CD player in our house or car!). I know families who listen to the CD while in the car, which is a great way to help your kiddos learn truth even during mundane activities like driving. You could also use the CD to help children learn how to have a personal time with the Bible each day, even before they are able to read (as they can listen to the CD while looking at the book).
The Jesus Storybook Bible
I also love this story Bible. The writing is high quality and the pictures are even better (though I do suspect the drawings are the kind of art that will be seen as really outdated in 20 years, but we'll see.)
This story Bible is along the lines of other story Bibles, where various accounts from the Bible are retold in a story format. The subtitle of the book is "every story whispers his name" and this is definitely a theme throughout the whole book, how every story points to Jesus as the Main Story of the whole Bible. I appreciate that below the title of each chapter are the chapter references where the original account from the Bible can be found. I find that I am often even struck by the stories, convicted of sin or worshipping God for his goodness.
The one downside that I see to these retellings of Bible stories is that it is definitely written for a post-modern crowd as stories are very feelings-based and talk a lot about God's "heart" and how God is feeling. These things make this a more culturally-conditioned Bible storybook in my opinion (although of course all retellings of Bible stories will be culturally conditioned in some way, but this book seems strongly so). Some would also point out that the Bible was written to be understandable to the everyday person (as it was written in Koine Greek), so this could be part of the motivation of why this book is clearly aimed at a post-modern audience. It could be that this is the best way for a child that grows up in this type of society to be introduced to these stories, but I personally am always a bit hesitant when I see too much of culture seeping into something like this.
This story Bible is definitely for an older crowd. I read it sometimes to Esther (more because I like it than her, ha) but she gets bored pretty fast. The stories are long, and there are many words on each page, so I would say that four is the minimum age that kids can start getting something out of this book. This also means its usefulness extends higher as well, to at least age 8 or 9.
This book also comes with a CD, which we also have never listened to (see above) but I have heard a few of the recordings which have been made into YouTube videos, and the reading is high-quality. If I remember correctly, the reader is a fairly well known British actor. Here is an example of one of the videos that I mentioned, which will give you an idea of the writing style and illustrations:
If I had to recommend one of these two books over the other, I couldn't (unless the judgement was based solely on the age of the child). There is no reason to limit the number of quality Bible story books, so I recommend owning both, especially since each fits a different niche. Since neither book is the actual Bible, owning a few helps kids to see that these stories are retellings of the real stories, each of which might draw out different features or highlight different points.