Usually if you choose the application layer, you can design your app code to do the logging in a single point, that will handle consistenly all your historical table. differently triggers are a more complicated approach to maintain because they are (depending on the db technology) replicated for every table: in case of hundred of tables the amount of code for the trigger coud be a problem.
if you have a support organization that will maintain the code you are writing now, and you don't know who will maintain your code (tipical for big industries) you cannot assume which is the skill level of the person who will do fix on your application, in that case it is better in my opinion to make the historical table working principle as simple as possible, and the application layer is probably the best place for this purpose.
