So I've run into some trouble with finding out the best tire size to get for my 2001 XJ limited. I'm planning on getting a 3" lift and new 31" tires. I want to get Cooper AT3's but the actual tire diameter for the 31X10.5R15 is 30.2" and the width is 10.7" versus the 245/75R16 which has a diameter of 30.51" and a width of 9.6". So which is the better size? By the way I have 16" rims.
245/75R16
Diameter: 30.51
Width: 9.6
31X10.5R15
Diameter: 30.2
Width: 10.7

Well first off those 31s won't fit because they're for a 15" wheel.

And you're being too meticulous with this. That 0.3" is not going to have any noticeable difference. The 9.5" width might look a bit smaller than you want but idk what you're going for.

Completely disregarded the wheel size. Thanks.

What I'm going for is a tire that's going to look good with a 3 inch lift and perform well off road. I don't do any extreme off roading but I still want something that's going to be an all around good tire off road. Whether it's through snow, mud, or rocky terrain.

33x12:50x15's and any good M/T tire will work for you I found mine for just over $650 for 5 of them and you will need a 15x8" wheel with 3.75" of BS a steel wheel is cheap from Summit or Jegs $40 something bucks each. Here is that tire/wheel combo on a 3" lift with some trimming. The key to good off road performance is being able to air down your tires (need 8" wide wheel) for that then air them back up again before you hit the roads.