Well for me the only real reason i root is to use Titanium backup. It backup up All my apps and data every night to the SD Card, then my SD card in return gets backuped to my server though Titanium Media Sync. This way if i ever lose my phone all my data is in a safe place and i can go ahead and use SeekDroid to wipe my phone so all my data doens't get stolen or misused.
Rooting is up to you. I've been Rooting and flashing roms on phones for about 3 1/2 years now. My first Android phone was the Moto Droid X which was the first 4.3 inch screen phone to come out which is why i got it. No i have the Moto Razr HD MAXX and i still love it but some phones are just faster like the S4 and my GF just got the new Sony Experia Z1s which is really nice and water proof (Took some pics of Koi underwater at a local pond. Was pretty awesome).
If you want to know more or as more about the S4 and rooting though look here
http/forum.xda-developers.com/index.php
Then to the top right where it ask to type in your Phone type S4 and then select the one that applies to you and what carried (yes it makes a difference what carrier is it) and you can ask more about rooting and the if its worth it to you. Also might find better answers to your current question there. XDA is pretty much Android Central for any and all mods for android phones.
Also in some cases like my phone Rooting allows you to unlock the bootloader (Not all phones can be unlocked) that allows you to flash what ever rom you wish on there for any carrier as long as the phone will work on their network. Similar to Jailbreaking the iPhone. Even if you can't unlock the bootloader there are ways to get custom roms on there as well.