Default [Q] Restore Internal Data only?

I tried posting this on a slower forum, but figured this would be a much better spot.

My wife broke her screen yesterday, but luckily we have another one not in use that is the same model. I also tried Nandroid backup, but got an error at android_security so I tried something else.. I decided to run 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?