How would you calculate this? I would venture to guess that it is nearly indiscernible and that driving variations would more than surpass any loss/gain by using thicker/thinner oil in the axle.
I towed over 6K miles last summer fully loaded and in 100+ heat. I trust that Ford has done the vernacular and I will stay with 75w-140.
All of you should check here:
Axle Facts and look around.
My opinion is that gear oil viscosity should follow use/axle oil temp. A truck that is used lightly will have low axle oil temps and could therefore be fine in the 90 grade range. In one of the test shown on the Lubrizol site linked above is a comparison of axle efficiency between a 80W90 and a 75W90 and there were significant efficiency gains just between those two grades. There are other tests that show a greater difference between the 90 and 140 grades.
A typical 140 grade has approximately the same viscosity at 250F as a 90 grade does at 210F (the viscosity rating temp). At 210F, the 140 grade is 37 percent thicker than the 90 grade and this offers a significant increase in rolling resistance.
Since we are talking F150 axles, I can say that my own F-150HD (8200 gvw, 10.25 rear axle) has a diff temp gauge installed. Solo, at around 85F ambient, the rear axle temp stabilizes at 170-180F @ 65 mph on level ground At that temp, the 90 grade in the axle is running at approximately 140 grade viscosity (23.8 cSt). A 140 grade at that temp is running at just under 250 grade (39cSt). These are all calculations made on Mobil 1 gear oils, 75W90 vs 75W140 using the Widman calculator. The 80W90 mineral oil I use is about midway between the two synthetics in terms of viscosity using these various calculations but still delivers less drag than the 75W140 synthetic.
So, if your truck runs below 210F virtually all the time, you are wasting energy running a 140 grade oil. The only way to know this is by installing a diff temp gauge. If you go to a Mag-Hytec cover, you will find a port is there for a sender. You will also find the Mag-Hytec will knock a good 15F off the diff oil temp no matter what oil you use. In may tests, a syn vs a mineral (same base grade) was worth another 15F or so.
The highest diff oil temp I've seen thus far in my truck is 225F, so day to day 90 grade is my best choice. I generally don't tow long distances in the F-150 (under 100 miles) but if anyone can match my 36-ton tow record, let me know (two loaded grain wagons). I regularly tow a single fully loaded 350 bushel KillBros grain wagon... that 10.5 tons plus another ton for the wagon. As gnarly as that sounds, I can only legally do 25 mph (farm equipment) so, surprisingly, diff oil temps don't get all that high. At any load, diff temp goes up with speed.
To paraphrase J.B. Books' "If you needs six, load six!" Comment, if you need 140, then by all means run it. If you don't, you are simply wasting energy.
Finally, if you want to spend $22, order SAE paper 2005-01-3893 "The Effect of Heavy Loads on Light Duty Vehicle Axle Operating Temperature." This was a preliminary paper, I think, to some testing Lubrizol has been doing with lower viscosity gear oils that are highly additivized. They claim a 6.8 reduction loss of driveshaft torque when using a 75W85 gear oil vs a 75W90, and a 2.0 percent increase in fuel economy. Also, gear oil temps were reduced 40 degrees on a new axle. The light oil also passes ASTM test standards for full load axle durability tests with results similar to a 75W140 oil. Details on this test can be found in the Lubrizol white paper, "Lubrizol Tow-Proof Technology Imroves Durability and Cuts Fuel Consumption." Google it, I don't have a link.