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Both are good transmissions. Depends on personal preference too. Climbing, and missing a shift with a standard is nasty-with that much weight behind you. Yes it can happen, even if you can shift like an epileptic in control, and the synchro's like it too, then fine. Starting on a hill with that kinda weight might be interesting.
Seen a few guys hill climb, for fun 4wheelin, but they have to select the right gear, or else over rev, not enough momentum, or over gear and bog out-same for muddin. Pick and go, not many chances to shift.
Auto's don't hold back as good as a standard, going down hill, and auto's do rob horsepower. However the torque converter multiplies torque, about 2-1.
Sure you can bomb start a standard, but if you have to rely on that, then your truck is probably a heap.
The C6 is cheap to rebuild, and could probably be done with some know how-modifications are plentiful. The standards, if something goes wrong, other than the clutch and pressure plate, usually easier just to replace the transmission-normally the old 4speeds don't break, but wear gets everything. Been many a year since a new 4-speed stick has been built.
Some thoughts! Research!