I do not believe that you are applying the code correctly.
If you are running but two circuits- a single multi-wire branch circuit- then the chart you reference would be appropriate.
If your intent is to feed a panel, I believe that 250.66 is the appropriate chart, and the ground wire would need to be at least #8. You could actually be -depending on the size of the feed- in the goofy situation where the ground has to be larger than the neutral!
This "fourth wire" can be either insulated and marked green, or bare copper wire. It must be inside the raceway.
While your application may be simple today, there are enough other issues around the farm- stray voltage, other equipment, moisture, waste, animal damage, corrosive chemicals, etc- that I see little profit in taking advantage of any "short cuts."
You didn't ask, but if you did, I would say "Dig- and dig deep." I'd urge the use of pipe- either RMC or sched 80 PVC. I'd remind you to have a disdonnect on the outside of the barn. And I'd reccomend that everything, even inside the barn, be NEMA-3R or, better yet, NEMA-4 Too many little critters get into the electric as it is!
My approach is conservative- mostly learned in Chicago- but it has served me well in these days of "power quality" issues.