If you're going to spend the money on doing an engine swap, then I'd go for a 5.7 Hemi. You'd probably spend MORE money to get a pentastar installed in your JK in place of the 3.8 than getting a 5.7 or a 6.1 would cost you.
I'm driving a Dodge 3/4 ton rental truck right now, and I'm really liking that 5.7 so far. There are enough people that want to do Hemi swaps that multiple builders have come out with kits, and there are lots of places that have experience doing Hemi swaps.