Well, I would strongly recommend 4.56 or even deeper. If you drive 27 tires (normally stock are around that):
3.73 -> 27"
X -> 31"
So X resolves to 4.28, so if you grow one step, it'll make not much of a difference; 4.56 will change driving marginally; a 4.88 would be best for off-road use, but you should calculate your max RPM for all your gears and see if the setup pleases you. I have an Excel sheet designed for AX15/AW4 transmissions and fuel engines; you could use it to make the proper calculations for your engine/transmission setup and decide for the best gears.
In my case, I'll never put tires bigger than 32" on my XJ, it came stock with 3.07 gears and I'm going to 4.10; I don't want to go deeper as I drive alot on the highway and 70mph is necessary for me, but I want good off-road performance.
If you're interested in the Excel sheet, PM me with an Email Address I can send it to.
Regards