It depends on how you define a "complete backup"
Your contacts automatically sync to your Google account unless you select to save them on the phone with certain manufacturer
All of your app downloads and purchases are saved in the Play Store (or the Amazon App Store) Same with any music, books, or videos you purchase through Google.
All of your email is stored in the cloud (unless you setup an account as a POP account)
If you sign up with either Picasa or Google+ (both google services) you can automatically have your pictures and videos uploaded and synced. You can also manually copy to a computer.
If you use Chrome (a Google app) then your bookmarks are sync'd
Ok, so what isn't sync'd...
Call log (don't think iTunes syncs this either)
SMS/MMS messages (don't think iTunes syncs this either)
Local files you stored on your phones like downloads and anything you put on there manually, but you can manually copy these files to a computer (same applies to iTunes, right)
Bookmarks if you're not using or can't use chrome, but you might be able to export them
App data! This is the big one because you can't save your progress in games, app settings, or anything stored within the apps (I'm pretty sure the iPhone has this same problem.)
Phone settings / Home screen setup ... can be a pain to have to re-setup everything (does the iPhone even have settings
)
As you can see, most of the important stuff is backed up and automatically sync'd. I'm pretty sure Andoid's backup is almost as robust as the iPhone's, but it's not quite as elegent because it's in a lot of different apps.