Found the answer to my own question elsewhere after chasing some links. In case anyone else needs a reference to how different weight diff oils affect 4x4 performance:

DIFF OIL
THICKNESS CHARACTERISTICS

Front
Thinner
• Increases steering into corners (off-power)
• If oil is too thin the steering may become inconsistent,
especially it can lose forward traction (and steering)
during acceleration out of corners
Thicker
• Increases stability into corners during braking
• Increases steering on-power at corner exit


Center
Thinner
• Front wheels unload more during acceleration
• Decreases on-power steering (reduces oversteer)
• Easier to drive on rough tracks
• If a high-power engine is used you could waste too
much power and sometime “cook” the oil in the center
differential because it “overloads”
• More off-power steering
Thicker
• More all-wheel drive effect
• Better acceleration
• Increases on-power steering (reduces understeer)
• Better suited on high-bite, smooth tracks
• Car can be more nervous to drive especially if a high
power engine is used - you might need to be smooth on
the throttle


Rear
Thinner
• Increases cornering traction
• Increases steering into corner
Thicker
• Decreases rear traction while cornering
• Reduces wheelspin