I have just been having the same trouble trying to update a friends iPhone and have (after much hair tearing) resolved it and restored the iPhone successfully with all settings, messages, contacts, apps and photos!
I was upgrading an iPhone 4 on iOS 4 dot something or other to iOS 7.
After the sofware update, the iPhone showed the Hello message and setup screens. So I did the following:
1. Tapped next on Hello screen
2. Selected Restore from iTunes Backup
3. Connected the phone to iTunes on the laptop
4. Selected the correct Backup and clicked Restore.
5. Here the iPhone itself said something like Restoring (can't remember exactly, but after it finished the phone turned itself off and came back on again with a small progress bar showing.
Then the progress bar went away and the phone appeared to be restored (showed app grid). On iTunes on the laptop the progress bar still showed the progress of 5 steps of syncing contacts, notes, music etc and finally photos.
6. Once the syncing was complete the iPhone showed the Hello screen and Setup menus again.
This was where the hair tearing out started... and I went into a loop of Restoring from iTunes backup, syncing and Hello and set up screens... same again...and again...
When I clicked the top button on the phone to lock the screen I could see the photo that had previously been the wallpaper on the phone so I knew at least the photos and stuff were on there.
What I did next to finish successful restore:
1. Clicked next on Hello screen
2. Chose Restore as new iPhone (or whatever the wording is for that option)
3. The iPhone then brought me through the screens to set up an iCloud account and input my wifi and email settings etc.
4. After these setup screens were done, the phone was fully restored with all contacts, messages, photos and apps etc.
So I was stuck in a loop for ages thinking that it hadn't applied the backup, when it actually had, but it just needed me to set up iCloud etc to finish the restore on iOS 7.
I hope this helps someone, even if it is too late for those on this thread.
So glad to have found your post, dredmo! Have spent HOURS going round in circles repeatedly 'restoring'!!!
Following your advice, when I got to the point "Set up your Iphone" - instead of selecting 'Restore from ITunes Backup' (which I had done umpteen times previously) I selected 'Set up as new Iphone' and followed instructions from there. Success at last!
Thank you, thank you, thank you!