Go with what interests them and what they can comprehend. I know sometimes mine can physically read it but don't have the background enough to comprehend exactly what is going on. For example, if you kiddos don't have a background in pioneer life, the vocab in LHP series might confuse them (unless they're reading to you so you can explain along the way). I'd say keep their independent reading where their comprehension level is and have them read the harder things to you (or Dad, etc).
Or at least that's what I try to do. My oldest is an advanced reader, as a 4th grader....her favorite book recently is The Witch of Blackbird Pond. This was supposed to be read aloud but she read it herself. It's considered a Middle School book for Lang Arts purposes (if you try to get a LA guide on it, etc). She reads anything from a 3rd grade level to 7/8th grade. She could probably read higher but the content is too old for her so I limit her reading to "mommy approved" titles