No, you probably couldn't burn out if you had to. Weight = traction. Balanced weight = more traction.
It is harder to spin tires on anything with more weight on it... that is more traction. Why else do people put sand bags in the back of their pickups in the winter? Why else do they increase the weight in the weightbox on the sled as the weight classes go up at a tractor pull? Why don't they just pile all of the weights on the tractor at the same place if balance doesn't matter? (you want to keep them balanced side to side as much as possible, and only enough on the front to keep it down, you want all the weight you can get on the rear drivewheels)
With a 2wd truck and a full 17 gallon tank, the driver side wheel (without the driver) has 100 more pounds on it than the passenger side. Notice that when you spin a rear wheel most of the time it is the passenger side, locking the rear axle elimates this. The engine and transmission are obviously centered between the wheels so the weight is balanced between the two, the wheels are in more equalibrium and less likely be dominant on one side. It is also obviously heavier than a fuel tank which = more traction. In a 4x4 the front wheels are turning under their own power and help loose ground keep moving instead of balling up in front of nonpowered wheels. I have seen 2wd trucks stuck just because of that reason, they couldn't push the crap that built up in front of the front wheels that were not even turning... makes them mighty helpless in a hurry.
Weight has everything to do with it and trying to push the heavy end with the light end will not work as well as a 4x4 that is at least trying to do something with the heavy end.
Not to mention a little thing the Air Force refers to as "Thrust Vectoring" where you can use the front wheels to pull the front end where you want it rather than use them as rudders which only do something when you are actually moving.
I would gladly take on a locked 2wd truck with my open 4x4 with the same tires... I even have a nice snowy field with a tractor close by to pull it out.
The only exception to this is desert racing, which is worthless to worry about in my part of the country. The closest thing we have to a desert is the sand covered streets after the snow melts.