I have gas and diesel engines around here big and small, and I can't think of ANY time the diesels aren't better on fuel!, loaded or not! This is REAL world experience, over many years of owning them.
I never said any where that diesels we not more fuel efficient at any load, I said their advantage ERODES(gets smaller) at light loads.
When you look at gallon per (what ever time or distance measurement of your choice) then yes a diesel is nearly always more fuel efficient. When you measure grams(or ounces) of fuel burned per hp hour the measurements get much closer at lower loads. Diesel still wins by a high margin at higher loads. Diesel fuel(7.2 lbs per gallon) is heavier than gasoline(6.2 lbs per gallon). Therefore diesel has more btu's per gallon. 129500 for diesel and 114100 for gasoline.
If you look at all the old literature for caterpillar when they brought out the first mass produced mobile diesel it mentioned nothing of its fuel efficiency (which it did have) but about its fuel cost for a day. Diesel fuel for many decades was a byproduct that was priced dirt cheap. As was LPG when it came out(remember all of the propane tractors in the late 50's). People are trying to do the same today with LNG. Because most business could give a crap about MPG, they care about Mile per Dollar.
I will use this page as info as local prices vary widely.
http://fuelgaugereport.aaa.com/?redirectto=http://fuelgaugereport.opisnet.com/index.asp
Gas at 3.48 and diesel at 4.09 for average price. You get 32787 btu's per dollar for gas and 31662 btu's per dollar for diesel. Add in the higher operating and maintenance cost(initial purchase cost, oil change cost, fuel system maintenance cost) for diesels and unless your fully burdening the machine you will not have a positive "financial" advantage. Notice the financial part and fully burdened part!
Try a long term analysis of a gas vs diesel pickup and unless you are pulling a good size trailer all the time the diesel is costing you more money. This is especially true with the new diesels catalytic converters and particulate filters adding thousands to the purchase price and more maintenance down the road (but didn't work either when I did it back in the late 90's for Dodge 2500 truck and 90 cent diesel) and gasoline engine finally getting direct injection and low speed boost turbocharging(opposed to previous turbo cars set up strictly for higher rpm boost/performance)
Now please don't take this as I am trashing diesels, I am not. I understand that they are nice in many ways. I have a Cat powered Chevy 6500, the high torque is nice for towing my 38' horse trailer. I have had john deere and case diesel tractors and a cat dozer and driven all brands of diesel trucks and a lot of skid steers, all terrain fork lifts, combines, graders, ect. My day job is a machinist(used to assemble them years ago) for the largest diesel manufacture in the world, making parts for 750-7000 hp diesels (also natural gas engines) include one for the 777-797 haul trucks 992/994 loader,trains,ships, EPG, and NG compression. We sell very few stationary Diesel engines anymore in North America, they want the NG version and all the end users are wanting LNG versions for the mobile equipment industry wide due to lower fuel cost(even though it gets lower MPG, or should I say GPMile for this size equipment).
Now since this day in age lawyers are abound I have to post this.
The above is my opinion and not the statements of my employer.