Four claws show more stone. Six claws lose fewer of them. That is the trade, and which side you want depends on the stone and on the hand.
The case for six
With four claws, one failure is a lost stone. With six, one failure is a service. On a ring worn daily, particularly on a hand that works, six is the answer nearly every time.
The case for four
A four-claw setting covers less of the girdle, so a stone under a carat looks meaningfully larger. On a ring worn occasionally, that is a real gain for a small risk.
What we will not do
Three claws. It looks wonderful in a drawing and it is a stone waiting to fall out.
