Transferring apps to new iPhone? I just got an iPhone 6, upgrading from the 5.

My main computer is a Mac Pro Running Snow Leo, and iTunes 11.4. I backed up the iPhone 5 and when I went to sync to the 6, I got a warning that it wants a higher level of iTunes. I went to the other Pro running Yosemite and iTunes 12 is there, so I backed up the 5 to that computer. The apps don't show up to add back to 6, nor does the 5 backup show to copy it over. 

How do I get the apps to transfer? (If I need to transfer all of iTunes from the Snow Leo Mac to the Yosemite Mac, and just update iTunes in place, that's ok too. I'd just like a hint at the best method to get this new phone up and running)
Since iTunes won't back up the apps, I tried taking the files, e.g. Evernote 7.9.1.ipa, etc, and moving them from the iTunes 11 to iTunes 12. 

When at the Yosemite machine running iTunes 12, a double click of the app loaded it to the folder where apps are stored and pulled it into iTunes to sync. 

Now, I'll spend a bit of time and look at the old phone to see which apps I use and would like to keep. Just a click to load each one, at least not a search and download off the store.