I dont believe that one certain type of attachment will cause a higher well-being later in life. Although it does play an important part there are other equally if not more important factors that play a role into the social development and habits of a child. For example the economic status of his upbringing, the psychological and social backgrounds of the caregivers, experiences during the critical stages of a childs life and to some extent, genetics as well. All these situations factor into the later outcome of a child and isnt solely dependent upon the attachment to the caregivers in the early stages of cognitive and social development.
Although I think all the factors you mentioned would definitely affect the well-being of a child later in life, I think it could be argued that they actually affect the attachment of the child, which in turn causes high or low well-being later. The chain of cause and effect are fuzzy, but I think all these factors are inter-connected and work together to form the child's future.
