iOS Updating: OTA vs iTunes
Solution 1:
Yes at first approximation they are the same, but the mechanism of the update is different since one can be a delta and self-applied update and the other installs a complete build rather than patching the OS.
Digging deeper, the OTA update implies the OS and device is working properly, so Finder or iTunes is a good bet if you really want to ensure the update goes well or want to put the device into recovery mode to ensure the new OS and only the new OS is written. Obviously, if the device is having problems, you may opt for a computer to control the update rather than hoping the device stages, installs and executed cleanup of the patch properly.
Assuming your device is working well, you can safely update OTA and in many cases - the download is a delta update that is smaller than the entire image if you are doing an update that isn't a major version (4.0 or 5.0 which started the OTA capabilities and presumably 6.0 when it ships).
Using Finder or iTunes also gives you a chance to transfer purchases and reduce the number of apps you will have to re-download after a major update. Again, not an issue on incremental updates like 5.1.1 update from 5.1.
- iOS version history on wikipedia
- About iOS 5.1.1
In practice, this even has been called out as a deciding factor for the jailbreak that was first released for iOS 7 where the notes said the exploit won't work against an OTA iOS 7 device, and only against a cleanly restored device. I don't know if that has to do with the signing key or an actual difference in the two images, but it shows that the processes are indeed different in some respects.
Solution 2:
As @bmike notes, the processes are similar for OTA or iTunes. The OTA updates supply the deltas while the iTunes updates the whole build. The iTunes update also seems to run faster from my experience (purely anecdotal).
One big difference from my standpoint is the mandatory backup that occurs if you back up over iTunes - you can also transfer purchases and do any other management activities before the update. You can backup via Wifi with the OTA method as well, but that's a separate step that you'll need to explicitly kick off.