Default [Q] Restore Internal Data only?

My wife broke her screen today, but luckily we have another one not in use that is the same model. I ran titanium back up on her broken phone, factory reset the new one, moved the sim and sd to the new one, and tried to restore.

The problem I ran into is that there is not enough storage on the new one to cover everything from the old phone. Using titanium backup can I just restore the internal data, app data, and system data on to the new phone?

I also tried Nandroid backup, but got an error at android_security..