MyBackup will do batch.. Titanium is more in depth to where you have access to system files as well as application files. I like to use a combo of both apps. I use Titanium for backing up applications and freezing unwanted stuff.. and I use MyBackup for backing up/restoring call logs, sms, mms, bookmarks, alarms, etc. Both of these apps are very useful when you are flashing ROMs because you will need to wipe the phone out. So having these two apps makes setting the phone back up with all your stuff a lot faster. Having a rooted phone also gives you the ability to backup/restore not only apps... but app data as well.
You do not want to accept an OTA with a rooted device... worse case scenario, you soft brick your phone which could happen if there is unfamiliar files on the phone. What happens is the OTA tries to install, detects that something is different, doesn't know how to handle it and freezes.. the good news is that soft bricks are fixable. This scenario usually happens if you've rooted the phone and changed/altered a system file.
That's the worst case scenario... Most of the time all that will happen is if you accept an OTA, it will just cause you to lose root access.. In which you can usually just re-root the phone afterwards. So while it's not that serious, it's just safer to not chance it just in case the worst does happen.
What you'll want to do is.. 1)unroot the phone, install the OTA, re-root the phone (a pain in the ass) or 2)Devs will put out a version of the OTA that's safe to flash to a rooted device.
Benefits of a rooted phone:
*You can make a complete backup/copy of the phone (ROM/OS/Data) which is called a Nandroid backup. It's similar to creating a restore point in Windows in which you can always revert back to a previous state.
*You can back up/restore app data using apps like Titanium Backup.. never worry about losing progress made in a game, app settings, info, etc
*You have access to the entire registry/every single system file of the phone... freeze/delete unwanted bloat, apps, files.
*You can install custom ROMs.. complete customization of anything on the phone... added features, change looks, etc..
*Install custom Kernels.. boosts performance, ability to overclock/underclock the CPU, ability to undervolt which gives better battery life (combined with the other kernel tweaks).
*Receive leaks of OTA's weeks/months before the carriers release anything.
*You get free wifi tethering.. Turn your phone into a mobile hotspot for free (make sure you have an unlimited data plan

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There's a slew of benefits to having a rooted device.. I'm sure I'm forgetting some stuff, if I remember I'll add it to the list.