Well, good question!

Here are a few considerations that may help you decide. The Bible Quiet Time box is completely independent, while the BIble Study box is teacher directed.
For the Bible Quiet TIme box, dc use The Illustrated Family Bible, reading several pages from there on their own. Children probably need to be fairly strong readers to do that. They also memorize all of Phil. 2 and sing it along with a CD. Finally, they learn to pray using the ACTS model.
The Bible Study box must be done with the parent and uses Genesis Finding Our Roots. It is an excellent Bible Study on Genesis; it is quite meaty. We've talked about genealogies, how to figure dates of occurrences, worldview, different world accounts of the Flood, etc. It fits well with the Ancients time period, but also gives an excellent foundation for understanding the Bible, and how so much of it is based on Genesis.
I guess I'd lean toward having dd do CTC's Bible Quiet Time box when doing PHFHG's core (left page), and if you have time the following year, do Genesis with the 2 of them when doing CTC's core (left page). However, you will know best what you'd enjoy, and getting the manual will definitely help with that decision as well. Whatever you decide, we've really enjoyed doing both this year, so either one is a good choice!
In Christ,
Julie