Here is another way of thinking about it. With the 5.13, the four gears that the transmission has are more closely spaced between 0-55mph, therefore, the transmission is able to keep the engine rpm closer to its ideal rpm more of the time. With the 4.10, the four gears are more widely spaced between 0-80mph; so the transmission isn't able to keep the engine rpm as accurately close to its ideal rpm as much of the time. The advantage, however of the 4.10 is that it keeps the engine turning more slowly at 55-70mph, where fuel efficiency is better, and it doesn't need the extra hp on level ground. Going up hills, however, the more closely spaced gears are an advantage to keep the engine closer to its ideal speed.
2001 F350 XLT 4X4 crew cab, dual rear wheels, long bed, black, 7.3l turbo diesel, automatic transmission, 4.10, shift on the fly, running boards, sliding rear window, 38 gal fuel tank, Odyssey extreme 65-PC1750T batteries, Michelin LTX-MS2 rear tires, Sumitomo Encounter front tires, Shell Rotella Ultra elc, 11,500 gvwr, 20,000 gcwr, 7500 gvw, completely stock, 114,000 miles when purchased, now has 250,000 miles, repairs so far: two starters, batteries, cps, brakes, tires, alternator, ball joints, locking hub, wheel hub, AC compressor, serpentine belt, power steering pump, driver's side window, ignition switch, o-ring, Spectra premium radiator, water pump, fan clutch, fan blades, thermostat, thermostat housing, tensioner. Stolen twice so far, but recovered both times with major damage.
2005 Nomad Rampage toyhauler made by Skyline. 11,500lb gvwr.