You have received some good advice to ponder here.

I would print out the first week for PHFHG, and the first week for CTC. Really ponder the "I" boxes, and see if dd can do those things completely independently. Then, check out the "S" boxes, and see if dd can do those boxes with some help from you to get started, but then finish them out on her own. Here are links to the first week of each of these guides...
http://www.heartofdakota.com/pdf/PHFHG-sample-week.pdf
http://www.heartofdakota.com/pdf/CTC-First-Week.pdf
The level of reading material is higher and harder in CTC. I'd say "The Story of the Ancient World" is one of the harder history books dd will be doing. Here is a link to an excerpt from that book, so you can see if she can read and comprehend this well...
http://www.nothingnewpress.com/guerber/ancient26-27.pdf
Here is the first chapter of another one of CTC's history books...
http://www.heartofdakota.com/pdf/kemp_g ... review.pdf
In PHFHG, you read a portion of the history, and your dd reads the other portion. In CTC, dd would read her own history, so it is good to check if she's ready for that.
As far as LA goes, here is a sample of CTC's dictation...
CTC Level 5 Dictation Sample:
viewtopic.php?f=6&t=5068&p=37153#p37153
PHFHG has 1 x a week short creative writing lessons that are done with the poetry. CTC has 2 x a week creative writing lessons that are done with "Write with the Best". You can view part of the WWTB writing guide here...
http://www.edudps.com/WRITE-WITH-THE-BEST-Vol-1.pdf
PHFHG has very short written narrations, about 1-3 sentences, ending with around 3- 5 sentences. CTC has longer written narrations, around 5-8 sentences long, but CTC still does a great job of teaching written narrations at the start of the guide. The helps in the Appendix are wonderful.
Finally, here is a rundown in time allotments of the day for each of the guides...
CTC time it takes:
viewtopic.php?f=6&t=3765
PHFHG time it takes:
viewtopic.php?f=6&t=4244&p=31219#p31219
I hope this can help you choose what is right for your family. As you can see from the wise words of the 2 pp's, HOD is not a one size fits all curriculum - which I personally LOVE. You can make it fit your family like a glove, it just takes some well-spent time to figure out the best placement for your dd. Keep asking questions, and hopefully some of this will help!
In Christ,
Julie