You'll get more body roll but it will ride 10x smoother, especially off road. No more rocking back and forth over speed bumps, uneven driveways, etc. I use to drive both my ranger and sport trac on 33s with no sway bars the majority of the time.
The easiest thing to do is just remove on end link, and leave the other one on. It will disable it, but keep the bar from swinging freely and contacting the suspension parts. Re-installing only takes a minute or two if you want it back on. It is definitely worth pulling it off and trying it out. Run over the roughest patches of roads that you normally drive on, over some speed bumps and stuff, you'll see that it is smooth and you can go faster over the same things. The body roll isn't that bad, just don't drive it like a sports car. Good shocks help too.
When the front suspension can work independently, you'll actually get a little
bit of flex from it.
Same front suspension as your truck, sway with a body lift, sway bars disconnected;