However, in our case it is already lost due to SQL Server being turned off. hence there is no way those transactions can get saved into AC database. I am sure you will disagree.
It isn't the best way to do a backup anyway.
I'll let James answer as to the SQL 2012 internals, but my understanding is that in stopping SQL, memory is emptied by either committing forward or writing out pending transactions so that the end-state is ACID compliant, known to the parent database, and can be successfully mounted and started. Nothing known is lost.
"Best" depends on the skills, access, knowledge, and aptitude. Not everyone has what is required to do SQL .BAKs, or to schedule full and differentials.
As Dirty Harry says, "A man's got to know his limitations."
