When does it help to restore an iDevice using iTunes, as opposed to "erase all content and settings"? There are two ways to factory reset an iDevice:


On the iDevice, open Settings > General > Reset > Erase all content and settings. (Reference)
Plug in the device to a computer, open iTunes, and click the Reset button. (Reference)


One difference between these two is that (2) causes iTunes to download and install a fresh copy of iOS. Obviously, you'd use this technique when your iOS installation is so messed up that it doesn't even boot.

What are the other situations in which there's a difference between these two techniques for performing a factory reset?

Concretely, my iPhone suffers from poor battery life. I've exhausted all the other options I can think of, and I'm about to do a factory reset. Is it better I do it using iTunes in case my iOS installation is corrupt in some way?

I don't want to be in a situation where I do a factory reset on-device (technique (1) above), find that it still doesn't solve the issue, and then have to (2) anyway. If there's a chance of that happening, I'd rather go straight away to (2). Thanks.
Erase all content and settings does exactly that, it erases user data and restores default settings - but leaves the current version of iOS intact.

Performing a full restore through iTunes is the only way to completely erase the device and perform a fresh installation of iOS.

If you've any doubts then the iTunes restore is probably your best option as it will update your version of iOS, with the option of backing up and subsequently restoring your apps, music and other settings with the minimum of effort.