You might want to take a close look at your front derailleur too.
1. Make sure the seat tubes of both bikes are the same diameter (probably).
2. How does the front shift cable go? Top tube cable routing says "top pull front derailleur" to me. Down tube cable routing says "down pull". (Probably ain't gonna work,)

Does the new frame come with a seatpost? This is another place where you might luck out but, unless you are luckier than me, I wouldn't bet on it.

So far as cables and housings go, you're moving everything over to a bigger frame, right? Bigger frame means longer cables.