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:

1. On the iDevice, open Settings > General > Reset > Erase all content and settings. (Reference)


2. 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.