At 4" of lift with 33" tires you are going to feel different driving down the road, particularly on curvy roads. I personally don't mind how mine handles even with a looser sway bar. I can keep up with most vehicles on curvy mountain roads no problem without feeling tippy. I can also cruise 70mph down the freeway and let go of the steering wheel. I have a good tight steering and well balanced tires though.
Don't forget though when you go to bigger tires you are very likely going to NEED to regear your Jeep. For what you want to do with your Jeep you're likely better off going with a 1-2" lift with 31" tires where your current gear ratio (depending on what you have now) is likely to be more acceptable. With the 3.07 ratio and the 5 speed transmission in my Jeep when I bought it I never used 4th-5th gear. I've since regeared to 4.56 and almost wish I would have went 4.88 for the amount of freeway driving I do. Now I only use 1st gear when on a hill or when the Jeep is really loaded down, otherwise I take off in 2nd to save a shift halfway through the intersection. (On the other hand the previous owner had no issues with how it drove even before I fixed the suspension and steering when it was freaking scary doing just 55mph)
what i have now is 31x10.5 and dont think there is a lift. I dont like the 31.
Is it really necessary to regear when running 33"? Didnt think so.