If you were going to Moab I would hope you have brains. I went so far as to axle swap a Dana 35 for a Dana 44 simply because being stranded out on a trail due to breaking a Dana 35 shaft and possibly damaging the goods in a differential can be as much as a $2,000 tow bill (+ repairs and a ruined week). But then again, the tow companies are in business for a reason, so if you want to help keep them in business, be stupid.
I agree to some extent that TJ, JK, JKU, JL capabilities vary based on tire size and departure angles/clearance. I.e. a TJ on 33's is probably as capable as a JKU on 35's, maybe a tad more, but other issues are involved. I've seen JKU's without lockers do pretty amazing stuff just because of the extra weight and the traction control system or the hill descent button. There are other factors, but the bottom line is I've come to think it's more complicated than simply tire size.
Once you get locked you are on your way to glory, but tire size does matter, larger tire rolls easier over obstacles, and those with an overhang are only overcome by a tire that can avoid getting pulled under the lip, then there is tummy clearance, which can be a factor on certain obstacles. I have been high centered and my Jeep twisted like a top until a tire hit a rock.