I'll throw my two cents in, since I've had two g4s.
First off, you may or may not be *able* to root, depending on which firmware you have. My first G4 came with Android 5.1, which was rootable. I received a warranty replacement (hardware issue) about a month ago that came with Android 6.0; that one is not rootable yet and probably never will be. This means you will likely have to forego any security updates for your phone. My warranty replacement has had two security updates since I received it.
I do not notice any particular performance difference between the two phones observationally. I never ran any type of benchmark on either one so I can't say for sure that their isn't a slight performance difference between them, but it certainly isn't obvious in normal usage. I use Nova Prime as my launcher, and it runs just as smoothly on the new phone as on the old one.
The main advantages of rooting for me were de-bloating and ad-blocking. You can run Greenify without root, but it does a better job on a rooted phone. And you can't use Titanium Backup to remove bloatware without being rooted. I'm still a little shocked at how many ads I get now that I'm not running an ad-blocker; I guess I've lived a sheltered life for a few years now
One major disadvantage I noted about being rooted is that you cannot use Android Pay. This may or may not be an issue for you; I mostly used Google Wallet for loyalty cards and rarely for actually purchasing stuff, so it wasn't much of a problem for me. I just used an older version of Wallet for my loyalty cards, that worked as long as I didn't attempt to use a payment option.
That's pretty much it from my perspective. There are a few other things you can do with root, but for my personal use case they were all minor. I never felt the need to install custom ROMs on my phone; I'm not sure it was actually possible with this device. I'm pretty sure that once you update past 5.1 you can't roll back, meaning you are stuck without root. So basically, you need to first determine if your phone is capable of being rooted, then decide which features are most important to you. Everyone's opinion will be different on that last point.