It's all a matter of context and style. Personally, I don't find the second sentence that much better. (Ok, it is a bit more tidy, but chances are that I wouldn't have perceived any difference during a casual conversation)
However, as I mentioned already, it is a matter of style and context. So, it depends on whether you write a letter to your manager or an email to your friend.
In my humble opinion, both sentences could be improved. What I would change in both would be the prepositional phrases at the end.
1. I need to look at some sentences from some favorite passages and break them down for the grammar value.
2. Grammar value is important to my writing so I need to look at some favorite passages for structure.
How about something like that:
3. Grammar is important to my writing, so I need to look at the structure of some favorite passages