I wrote a little class that is doing what you want, you can test it here.

Only thing that is different from your proposal is that I don't consider

[1,[{c: 1},2,3],{a:'hey'}]

and

[{a:'hey'},1,[3,{c: 1},2]]

to be same, because I think that arrays are not equal if order of their elements is not same. Of course this can be changed if needed. Also this code can be further enhanced to take function as argument that will be used to format diff object in arbitrary way based on passed primitive values (now this job is done by "compareValues" method).

var deepDiffMapper = function () {
  return {
    VALUE_CREATED: 'created',
    VALUE_UPDATED: 'updated',
    VALUE_DELETED: 'deleted',
    VALUE_UNCHANGED: 'unchanged',
    map: function(obj1, obj2) {
      if (this.isFunction(obj1) || this.isFunction(obj2)) {
        throw 'Invalid argument. Function given, object expected.';
      }
      if (this.isValue(obj1) || this.isValue(obj2)) {
        return {
          type: this.compareValues(obj1, obj2),
          data: obj1 === undefined ? obj2 : obj1
        };
      }

      var diff = {};
      for (var key in obj1) {
        if (this.isFunction(obj1[key])) {
          continue;
        }

        var value2 = undefined;
        if (obj2[key] !== undefined) {
          value2 = obj2[key];
        }

        diff[key] = this.map(obj1[key], value2);
      }
      for (var key in obj2) {
        if (this.isFunction(obj2[key]) || diff[key] !== undefined) {
          continue;
        }

        diff[key] = this.map(undefined, obj2[key]);
      }

      return diff;

    },
    compareValues: function (value1, value2) {
      if (value1 === value2) {
        return this.VALUE_UNCHANGED;
      }
      if (this.isDate(value1) && this.isDate(value2) && value1.getTime() === value2.getTime()) {
        return this.VALUE_UNCHANGED;
      }
      if (value1 === undefined) {
        return this.VALUE_CREATED;
      }
      if (value2 === undefined) {
        return this.VALUE_DELETED;
      }
      return this.VALUE_UPDATED;
    },
    isFunction: function (x) {
      return Object.prototype.toString.call(x) === '[object Function]';
    },
    isArray: function (x) {
      return Object.prototype.toString.call(x) === '[object Array]';
    },
    isDate: function (x) {
      return Object.prototype.toString.call(x) === '[object Date]';
    },
    isObject: function (x) {
      return Object.prototype.toString.call(x) === '[object Object]';
    },
    isValue: function (x) {
      return !this.isObject(x) && !this.isArray(x);
    }
  }
}();


var result = deepDiffMapper.map({
  a: 'i am unchanged',
  b: 'i am deleted',
  e: {
    a: 1,
    b: false,
    c: null
  },
  f: [1, {
    a: 'same',
    b: [{
      a: 'same'
    }, {
      d: 'delete'
    }]
  }],
  g: new Date('2017.11.25')
}, {
  a: 'i am unchanged',
  c: 'i am created',
  e: {
    a: '1',
    b: '',
    d: 'created'
  },
  f: [{
    a: 'same',
    b: [{
      a: 'same'
    }, {
      c: 'create'
    }]
  }, 1],
  g: new Date('2017.11.25')
});
console.log(result);