Question [Q] Transfer existing apps/data from old X to new X?

Hi all. I did a search but couldn't find a clear answer to this particular question. If it's out there I would appreciate if you could throw me a link.

I just received a replacement Moto X for my current unit which has a bad camera. Both were created using Motomaker if that makes a difference.

I've got the new phone activated and used Migrate to move the basic stuff, but I can't seem to find a way to move the majority of my apps to the new phone (I've used Titanium Backup previously but I guess that's not an option here as both have 4.4.2) and I've got quite a few programs that contain settings and data that I really don't want to lose or have to recreate from scratch.

Is there a program that would allow me to move the bulk of my current apps and the related data to the new phone relatively easily or should I just start the copy/paste bucket brigade via USB and my computer?

Edit: I'm also open to using adb and a nandroid backup if that's a possibility, but I would appreciate pointers to instructions if they exist. Thanks.