Something like:

Insert Into TableB
(
   TableName,
   cola,
   colb,
   colc,
   user_name,
   action,
   deletion
)
Select
   TableName,
    cola,
    colb,
    colc,
    suser_name(),
    'INSERT',
    GetDate()
(
Select 'TableA' As TableName, cola, colb, colc From TableA
Except
Select TableName, cola, colb, colc From TableB
) X
Drop TableA

Wrapped in a sensible Try/Catch handler just in case something goes wrong.