collection A :
 {
 "_id" : {
 "total_date" : {
 "total_date" : "2017-09-13 00:00:00.0",
 "stock_group" : "AC_01"
 }
 },
 "cnt" : 72.0
 }
 
 collection B:
 {
 "_id" : {
 "total_date" : {
 "total_date" : "2017-09-13 00:00:00.0",
 "stock_group" : "BB_01"
 }
 },
 "cnt" : 72.0
 }

Currently MongoDB has not provided an effective operator to support this requirement, but it can be achieved through code (js, python).

In [12]: def flattern(d):
 ...:     def _flattern(src, dst, prefix=''):
 ...:         for k, v in src.items():
 ...:             key = k if prefix == '' else '{}.{}'.format(prefix, k)
 ...:             if isinstance(v, dict):
 ...:                 _flattern(v, dst, key)
 ...:             else:
 ...:                 dst[key] = v
 ...:     result = {}
 ...:     _flattern(d, result)
 ...:     return result
 
 In [13]: d1
 Out[13]:
 {'_id': {'total_date': {'stock_group': 'AC_01',
 'total_date': '2017-09-13 00:00:00.0'}},
 'cnt': 72.0}
 
 In [14]: d2
 Out[14]:
 {'_id': {'total_date': {'stock_group': 'BB_01',
 'total_date': '2017-09-13 00:00:00.0'}},
 'cnt': 72.0}
 
 In [16]: for k1, v1 in flattern(d1).items():
 ...:     for k2, v2 in flattern(d2).items():
 ...:         if k1 == k2 and v1 !  = v2:
 ...:             print('k1 => v1: {} => {}'.format(k1, v1))
 ...:             print('k2 => v2: {} => {}'.format(k2, v2))
 ...:
 ...:
 k1 => v1: _id.total_date.stock_group => AC_01
 k2 => v2: _id.total_date.stock_group => BB_01