Confusion about iPhone Backup/Restore

[rgG]

My daughter just got a new 5S.
She backed up her 4, running iOS 6.
Nothing she tried would let the new phone restore from her back up of the 4. A new back up she made just before trying to set up the new phone.
She apparently even tried updating the 4 to iOS 7, but that didn't work either.
Then she tried to back it up to the cloud, so she could restore from that, but her 4 would not back up to the cloud.
She finally had to download an app to get her contacts to the new phone.
She was not happy. Took forever, and never did work.
Luckily, she has all her contacts backed up to Google, since she had an issue a while back with losing all her contacts even though she supposedly had them backed up to the cloud.

I have been having to trouble shoot weird data usage with my mother-in-law's new 5S. It has been just ridiculous and I am still not sure I have it solved.

I may just keep my 4 till it dies. Sometimes the price of upgrading is just too high.

Glad it "just worked" for you.
I think part of my daughter's problem is that there is some sort of issue with her old phone, since it lost all her contacts about a year ago. It has worked OK, but it seems to have issues with the cloud. Hopefully this new phone will be better.