在js中，比较两个数组对象中的children对象中的值并将它们的相同元素和不同元素分别提取出来

可以通过循环遍历两个数组对象，递归比较它们的children对象中的值，并将相同元素和不同元素分别存储到新的数组中。具体实现如下：

const arr1 = [{id: 1, children: [1, 2, {id: 3, name: 'A'}]}, {id: 2, children: [4, 5, {id: 6, name: 'B'}]}, {id: 3, children: [7, 8, {id: 9, name: 'C'}]}];
const arr2 = [{id: 4, children: [1, 2, {id: 3, name: 'A'}]}, {id: 5, children: [4, 5, {id: 6, name: 'B'}]}, {id: 6, children: [10, 11, {id: 12, name: 'D'}]}];

const sameChildren = [];
const diffChildren = [];

function compareChildren(obj1, obj2) {
  if(obj1.children.length !== obj2.children.length) {
    diffChildren.push(obj1);
    diffChildren.push(obj2);
    return;
  }
  
  for(let i = 0; i < obj1.children.length; i++) {
    const child1 = obj1.children[i];
    const child2 = obj2.children[i];
    
    if(typeof child1 === 'object' && typeof child2 === 'object') {
      if(child1.id === child2.id && child1.name === child2.name) {
        compareChildren(child1, child2);
      } else {
        diffChildren.push(obj1);
        diffChildren.push(obj2);
        break;
      }
    } else if(child1 !== child2) {
      diffChildren.push(obj1);
      diffChildren.push(obj2);
      break;
    }
  }
  
  if(i === obj1.children.length) {
    sameChildren.push(obj1);
    sameChildren.push(obj2);
  }
}

for(let i = 0; i < arr1.length; i++) {
  const obj1 = arr1[i];
  
  for(let j = 0; j < arr2.length; j++) {
    const obj2 = arr2[j];
    
    if(obj1.children.length === obj2.children.length) {
      compareChildren(obj1, obj2);
    }
  }
}

console.log("相同元素：", sameChildren);
console.log("不同元素：", diffChildren);

这里的思路是，先循环遍历arr1数组中的每个对象，再循环遍历arr2数组中的每个对象，然后通过递归比较它们的children对象中的值。如果相同，则将它们存储在sameChildren数组中，否则存储在diffChildren数组中。最后输出这两个数组即可。需要注意的是，这里对children对象的比较使用了深度比较的方式，因为children对象中的值可能是嵌套的对象。