The 3.8 with the automatic transmission sucks, even with 4.10 gears and stock size tires. Upsize the tires and you're in even worse shape. A friend has a 2008 Rubicon that I've driven both stock and with 35's, and I'm not a fan. The transmission's ratios are horribly mismatched to the engine's output, and really give the 3.8 a bad reputation for being terribly underpowered.
The 3.8 with the manual transmission is absolutely fine. I found my Rubicon to be geared pretty low with 4.10 gears and stock tires (I usually started off in 2nd gear on the street) but upgrading to 33-35" tires puts the gearing spot-on. With 35's I pull most regular grades in 6th gear even towing my lightweight camp trailer. When I'm traveling in a group of mixed vehicles through the mountains, I'm not the slow one even when pulling my trailer on steep grades. To the contrary, my Jeep is one of the faster vehicles in the group, and with 6 gears to work with, I always have the right ratio available. I've never found myself needing any more power than the 3.8 provides.
Another friend of mine has a 2012 Rubicon, and other than its automatic transmission it's built nearly identical to mine. On steep mountain grades where I just hold the throttle to the floor in 4th gear, his transmission hunts constantly, with a big jump between bogging in 4th and then zinging in 3rd. Back and forth, back and forth between the gears, which he finds quite annoying. We have one long high-altitude grade that we frequently drive together; with both of our transmissions in 3rd gear, he can't meaningfully pull away from me. His 3.6 has slightly more power, but with the different gear ratios between our two Jeeps, in the real world that 3.6's 83 additional horsepower doesn't manifest in a substantial difference.
The 3.8 has more off-idle torque than the 3.6. The newer motor catches up by medium RPMs, but then walks away from the old motor in the high RPMs. The 3.8 feels like more of a "truck" engine, while the 3.6 is more of a "car" engine in how their horsepower and torque curves behave.
The 3.8 is an older, low-tech engine design. It's much simpler to work on than the 3.6, and Chrysler produced hundreds of thousands of these engines and worked out most of the "bugs" before introducing it to the Wrangler. Most of the "problems" with this engine seem to stem from Chrysler specifying an overly thin oil viscosity (5W-20) in the final years of this engine's production in an attempt to eke out a little bit better fuel economy. I run 10W30 and have had none of the oil consumption people have complained about, nor any other problems with my 3.8.
The 3.6 is a much more modern engine design, and as with most brand-new engines it had some "teething" problems in its first couple years which seem to be fixed now. The 3.6 is a great engine, but I wouldn't necessarily say it's a must-have. If you find an earlier Wrangler at a good price, don't be scared of the 3.8 (unless it has that awful 4-speed auto behind it). If you want a Jeep with an automatic, don't even consider a 2007-2011 model.
