def deep_compare(obj1, obj2):
    """
    >>> deep_compare({'1': None}, {})
    False
    >>> deep_compare({'1': {}}, {'1': None})
    False
    >>> deep_compare({'1': [1]}, {'1': [2]})
    False
    >>> deep_compare({'1': 2}, {'1': '2'})
    True
    >>> deep_compare({'1': {'2': [3, 4]}}, {'1': {'2': [3, 4]}})
    True
    """

    if set(list(obj1.keys())) != set(list(obj2.keys())):  # Objects have different sets of keys
        return False

    for key, value in obj1.items():
        if isinstance(value, dict):
            if not (isinstance(obj2[key], dict) and deep_compare(value, obj2[key])):
                return False
        elif str(value) != str(obj2[key]):
            return False
    return True