to dispute, fight, contend, strive
爭 centers on active opposition: disputing, fighting, contending, or striving against something or someone.
爭 is the traditional form of 争. It originally depicted two hands (爫 and ヨ) pulling on a rope or object (亅), symbolizing a struggle or dispute.
The top 爫 looks like a clawing hand, and the lower part suggests another hand pulling on a line. Two hands fighting over something: that's dispute and contention.
For ソウ, imagine two people in a dispute both shouting 'So?!' at each other: 'So?!' -> ソウ, as they contend over the issue.