It is my understanding that the BJU 2nd edition was updated and changed quite a bit from the 1st edition, however I do not own a 1st edition to compare for myself.

It may be worth a call to BJU to see what they say the differences are between the two editions.
Since we will be using the BJU text in its entirety in our guide, I think it would be much easier to have the edition that matches the HOD plans. We will be carrying the 2nd edition in our HOD store as part of a package that will also contain the needed full-length books your child will be reading as well.
We're looking forward to sharing our selections for real books in a coming sneak peek!
Blessings,
Carrie