More roll will often give you more grip.
But only in a sideways direction. - I.e it stops the car spinning out but loses you forward drive.
Look up traction circle theory.
With a diff as soon as you get enough weight transfer that the inside wheel starts spinning then the outer wheel is transmitting almost no torque so can produce a lot more sidebite. -
(It doesn't matter that the inner wheel generates no side bite as most of the weight is on the other wheel.)
If you don't get weight transfer then both wheels are equally loaded so you have maximum possible traction in a forward direction. - But because the tyre is generating forward traction you are losing side bite.
Obviously this is an over simplification and there are other factors such as wheel angle etc.
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