I have a 1998 E-350 on a cutaway chassis (DRW). (138" WB, around 10,000# when loaded.) Stock from Ford, it had a medium sized (diameter) front anti-sway bar and no rear bar. Previously I had had an E-250 van, and I felt it had decent handling in stock trim. This rig was a bit more like driving on a large ball... get too close to any edge (i.e. turn and thus force goes to a corner) and you started to roll. Or maybe you could say it was a bit like driving a mattress. Rig had under 50,000 miles on it so nothing was really worn out. It was not horrible, but I like vehicles that are fun to drive, and it wasn't.
Note that I'm not (yet?) an overlander, this rig is 2WD, and I have never really had a 4WD vehicle (presuming my old Tercel 4x4 wagon doesn't count) -- so this may not apply to that type of use. Right now gravel or forest type roads are the most "off road" I do. I'm also not sure by the pic if your rig is DRW or SRW. Anyway...
I started by putting good shocks on (Koni), and that helped, but it still wasn't fun to corner. I had previously put anti-sway bars on a daily driver car and loved the improvement, so decided that was my next move.
I went with Roadmaster bars front and rear. I'd have to look up the details but I think they were around 1.5" diameter each (original front bar was more like 1", IIRC). This improved the front but made the rear suspension really harsh. Very jarring over even small bumps that were never noticed before. Not acceptable.
I went back and forth trying various combinations and ended up staying with the Roadmaster front bar, but changing the rear bar to a stock E-450 bar I got from a junkyard (has to be DRW bar if rig is DRW). This is smaller in diameter than the Roadmaster bar, but of course larger than the no-bar the rig came with. This proved to be a good balance between much improved handling (fun to drive now) and only very slightly harsher (if any) rear suspension action. To find the bar I looked in one of the online sites that aggregates a bunch of junkyards and then called around. The one I bought was a couple of states away and I had it shipped. The total came to around $65 (bonus!). I did go with new bushings for the used bar.
With the addition/upgrade of the bars I went from "ugh" cornering to fun cornering. Whereas before (talking highway here) I felt like I needed to take posted corners at 5-10 mph under what the sign advised, now I can go the recommended speed or even 5 over and get the same feel. Essentially it is much flatter in the corners. I have not noticed any particular oversteer. Also there is less of the ... not sure what you call it but let's say you pull out of a gas station on a slight angle and so the rig "comes down" off the change in level in stages. Before, that would start a sequence of rocking back and forth (cue sound of things in rear compartments banging around). With the new bar setup that "damps down" much more quickly.
I realize this may not apply to off-road "four wheeling" (which I have not done) (looks interesting though!)
Edited to add: When I was going through this process, and initially got the "egad this is way too harsh!" result with the larger rear bar, I was told by a couple of people in the suspension business that harsh (rear) ride was not uncommon on the E-350/E-450 chassis, especially when not super loaded (super loaded being, say, a 15,000# 28' RV, which is not my rig at all). Apparently ambulances particularly complained. I can imagine why thinking about how harsh the ride was on the rear of my rig with the big bars, and imagining trying to start an IV or something on a patient back there. Yikes. So maybe the rear bar was not put on an ambulance to trade some cornering prowess for the ability to not stab people in unintended places while driving/doctoring? Apparently a new thing is parabolic rear springs, which are popular with ambulances. I thought I might look into them, but things turned out well enough (for me) with the E-450 bar that I'm not going to mess with it unless something changes in future. Also there are things like Sulastic Springs (which I may still consider) and More-Ryde rubber suspension additions. I'm pretty happy as-is with the combo I have now.