Save yourself the headache and do both
I have a 2011 JK Unlimited and I ran it with 35s on the stock 3.73 gears. My transmission was unable to find gears jumping in and out of OD resulting in catastrophic transmission temps. At only 28K miles, my transmission was toast. The fluid turned grey as a result to the aluminum inside the transmission began to pit. The chucks of aluminum would flow through the torque converter and get pulverized resulting in a shiney grey fluid. Luckily my dealership went to bat for me and Chrysler replaced my transmission with a brand new unit under warranty. I was given the advice that due to my tire size and overall weight (metal fenders, bumpers, etc) that my transmission is working too hard on the 3.73 gears. I got a ARB rear locker and 5.13s done at Northridge and what a difference. Im always in ECO mode even at speeds of 70MPH. I have so much more power and much happier. I also installed a transmission cooler and my transmission fluid never reaches 180 (which is normal op temps according to Chrysler), its always at 115-140 degrees. So my advice is to do it and do both at the same time.