I think it makes good sense to pick the tire you want based on traction, toughness, tread wear, or some other measure of performance, rather than whether it is a 12.50 or 13.50 width. Chose the tire you want, and then make it fit. An extra inch of width should be pretty easy to work with .
2017 Jeep Wrangler Rubicon Recon; 35s - no lift, Warn 9.5 XP-S, ARB Twin Air, SPOD
2017 Jeep Grand Cherokee Trailhawk (wife's Jeep)
2016 Ram Laramie 3500 Megacab 4x4; 6.7 CTD, Aisen, AEV Prospector conversion; 37s, 4.10s, Warn 16.5K