What are the pros and cons to updating iOS with a full install via iTunes versus a delta update via the Settings app?
Advantages of full install via iTunes:


Device will be synced and backed up automatically during the update process
If at location without Wi-Fi access (and without an unlimited data plan), won't use up (large?) portion of the monthly quota
Device will be charging during the update


Disadvantages of full install:


Tethered to computer for the duration of the update (unless using Wi-Fi Sync)
Full update could be significantly slower due to the large upgrade file download


Advantages of delta update via Settings:


Convenient - no need to be tethered to a computer while updating
Delta updates are smaller - with potentially shorter total update time


Disadvantages of delta update:


Users might not back up devices if prior to running the delta update - a potential issue if the update fails
Update process might use significant portion of the device's charge on the battery, running risk of corruption if the battery dies during the update
If device isn't at 50% power, the device can't be updated via the update process unless plugged in (per this article):



  To install these updates, however, you need to have at least 50
  percent battery life on your device, or have it plugged into a power
  source.


I'm sure this list isn't comprehensive, but it contains most of the issues that I can think of.