I've seen this question/debate come up many times in the past, and until 6 months ago I couldn't chime in with a fully educated opinion. Now that I've lived with my 2012 JKUR for 6+ months and have spent considerable time with a 2011, I can speak from an experienced position. There is a VAST, immense difference between the two, and I would never suggest keeping the old motor in favor of the two as long as $$ isn't your limiting factor. It sounds like you're in a position where the money isn't the constraint, and you probably have great resale on your 3.8 so sell it and upgrade for probably not a huge load of cash.
I think where a lot of people are coming from when they say the 3.8 "isn't that bad" are because (1) that's what they own already and don't want to or can't afford to upgrade to the newer one or (2) are on smaller or factory size tires which makes the difference not as exaggerated or (3) they live in a flat area without super steep and long mountains to drive up and down regularly.
I live in Colorado, so weekend drives are almost always up and down steep mountain passes. The 2011 I've driven has a 2" spacer lift with 285/70/17 Duratracs and is stock otherwise, and mine has a 3.5" lift with 315/70/17 Duratracs. The 2011 is CONSTANTLY shifting and looking for power and is tiring to drive. The 2012 kicks down to 4th pretty regularly and on the really steep hills down to 3rd, but it feels like it does so willingly and has plenty of power generally. It is also much much less work to drive, and gets substantially better mpg. The 2011 usually gets around 14 mpg city and up to 17 mpg highway, however I never get below 15 mpg in the city regardless of how I drive the 2012 and the highway mpg ranges from 19 to 23 mpg. Yes I said 23 mpg. With 35s. In the mountains. I'm shocked that no one has debated that point with me in a couple of other threads where I've posted it, but one trip with the windows up, AC on, cruise set at 59mph from Buena Vista to Denver (pretty significant elevation) I was able to get over 23 fully loaded coming back from camping.
It's your money to decide what you want to do with, but I would imagine that the 3.8s will depreciate a bit more once the diesel is offered in the JK and with the new redesign in a year. I doubt the 3.6 will take as big a hit because it's already a modern powertrain and performs very, very well. Also the interior on the older JKs looked dated when they were new, but they are looking far older now compared with the 2011+ interiors. The NVH has been decreased with the newer interiors, and it's a very functional comfortable vehicle considering what it is. My vote is to sell yours while you can get the best return on it, upgrade to a much more modern and efficient platform and start modifying it to suit your needs. What's going to be easier to sell in 5 years? A 5 year old JK or an 11 year old JK??
