The 392 has D44 front and rear. They're 1.5" wider than the standard Rubicon axles. My understanding is that they're also stronger, but I have not yet found details of exactly how. I suspect it comes down to axle shaft material and spline count.
I think Jeep had to figure out a way to keep the D44 alive, or else switch to the considerably more expensive D60. On a package that already adds a good $25,000 to the sticker, I can see why they wanted to stick with the D44. The solution they implemented makes sense. It uses the MP3022 transfer case. Now, this does mean that we give up the standard Rubicons 4:1 low range for the "regular" 2.73:1, but the 392 has enough grunt not to need the extra gear advantage. But it also means that Jeep was able to make the Wrangler 392 a full time 4WD system. Your options are 4WD Auto (with the TC deciding how to split power), 4H, and 4L. Splitting the power between the axles keeps them from exploding. The TC does have RWD capability, but by default it's not available to the 392-powered Wranglers. If you really want RWD, there is a $300 tuner that will let you do it. I've got it, and have reprogrammed a few things, but I'm not interested in the 2WD mode.
The standard is 3.73 gears and 33" tire. If it's ordered with the Extreme Recon package it gets 35" tires and 4.56 gears.
Mine has 37" tires and the 3.73 gears. I wasn't sure initially if I'd need to regear, but after putting a few miles on it, I'm going to leave it alone.
The standard 392 is 470HP/470tq. Mine has been tuned and according to my dyno app it's 500HP, give or take a few. I've not had it on a real dyno, but I've compared the app and dyno sheet on the Vette, and it's pretty accurate.
I'm not planning any major changes immediately. Some cosmetic stuff, like graphics, and some fine tuning of the engine and suspension, but that's it for now.