iPhone full Backup possible?

The full backup does not include:

• iOS itself (since that will already be on the other device),
• app bundles (since they will be downloaded from the App Store again).

App data is backed up even if the apps themselves aren't. It's as full of a backup as is available and will back up all of your data.

In addition to @grg answer, backups do not include Media Library (iBooks, iTunes purchases, music, podcasts). Also, app developers decide what to include in the backup, so it would be good to save all important data manually first if it's saved in some app.

p.s. Apps that store sensitive data (like 1Password) usually store it in keychain, so make sure to make an encrypted backup (even with some easy pass like '12345').