Kelly,

I cannot answer your question about non western cultures and HOD although I did a bit of searching. Hopefully someone can contribute something worthwhile regarding that. I can, however, comment on Sonlight and HOD.
For what it is worth there is a lot of overlap in that many of the same books are used. I am referring mainly to what Sonlight calls "read alouds" and "readers" and what HOD refers to as "story time" and "DITHOR" books (used in the reading program called Drawn Into the Heart of Reading). To get a concise list and see what books are used where you'll have to do some old fashioned cross referencing with the catalogs.

In my limited experience with Sonlight (we have used 4 Cores) it is my personal conviction that HOD is better at assigning literature at an age/level appropriate time. This is of course a preference and you may not find this to be true in your family. Beginning with Core K I found that there were titles that were age/level appropriate and some that were not. This begins to happen more and more with Sonlight as the years go on. In fact, after about Core 2 I would highly advise researching and/or pre-reading books that SL suggests.
I have decided that IF I pull literature ideas from Sonlight lists after about Core 2 I will pre-read those books UNLESS they happen to be used in HOD. Hands down, I prefer the way Carrie has scheduled the literature. Really. She is a master at it and it's a HUGE draw to Heart of Dakota for us. I feel that I can trust her implicitly in this area. Pre-reading will happen only because I WANT to do it but not necessarily because I feel I need to screen content in HOD. To each his own of course because not all of us think or feel the same way about these sensitive issues.
I love Sonlight's catalogs and the beautifully arranged Cores. HOD does the same thing only better.

You end up with a fabulous guide and MEATY books. Using DITHOR gives you the opportunity to expand on your children's exposure to great literature in ALL genres. (There is always time to slip in a missionary biography a la Sonlight if you desire. We love to read SL's suggestions for missions/missionary stories. They make great extras for weekends, breaks, summer, etc.) Carrie ties everything together for you and if you spend time poring over the catalog you will begin to see how deep and rich the progression is in HOD.
Have you used the placement chart to place your DD?

I ask because with HOD you place a child based on their skills and not on content (what historical time period you prefer). HOD is integrated with skill work throughout each guide and the placement chart will help you to accurately place your kids. You probably already know that since you're using Little Hands to Heaven so this is just a friendly reminder

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