We do some of both.
We use the Heart of Wisdom Bible Study, Singapore Math, WinterPromise for history (and this year also for science), and Spell to Write and Read for LA. I am looking for a good introductory writing (composition) program for 3rd-4th graders. If you know of one, let me know. SWR does teach sentence structure and grammar, but it only teaches writing up to about the 3rd grade level. I have access to Rosetta Stone, but it is not working out for us right now. I like it and think it's a great way to learn languages, but Spiderboy gets bored with it. Go figure. I am glad I didn't purchase it!
BTW, Spiderboy has announced that he no longer wishes to be an astronaut. He wants to be a computer graphics designer for animation (in movies as well as games).
I think we started Learning Language Arts Through Literature at that age. It was a literature based program, sort of - every few days you'd have a passage from a book to copy, and then activities relating to the passage. You'd get three or four passages from a book and the idea was the kid would read the book on his own. There's a whole series of them and I think it goes up through high school.