How can I back up my App Data?

How do I back up App Data from my 4S 64GB in order to transfer it to my 6S 128GB (when it gets here)?

The issue I have is that over 50GB of App Data is stored on my iPhone, spread across 205 Apps.

The content either never was, or is no longer available on iTunes via my PC - how can I back this up so I do not lose it?

Everywhere I turn, I get told "iTunes can't/won't do that!" It's so infuriating!

I've had my 4S for nearly four years now, and now I go to upgrade and it seems that Apple software cannot actually make a 'proper' backup of user-content? Is that true?

Are there any programs that can?

Regards,

Susi xxx

(BTW *AVOID* AnyTrans Pro 4.7.0 [build 20150917] - I bought it last night, and it is so very busted. Despite saying that it will back up App Data, in it's current form it is no better than the results I have been getting with iTunes)