Both are valid methods of booking and ticketing. A TA will charge a service fee, whilst the airline won't. It might be worth booking with the airline directly if you've planned the whole thing out already. However you do get benefits like a longer ticketing time limit, better chances of clearing waitlists (maybe) etc if you book through a TA.

Additionally you can also pay the ticket via AA in Canada at the Japanese pricing. This might be a better option than calling up AA Japan, particularly if a paper ticket is required. AA Japan will not issue paper tickets over the phone whereas Vancouver is only a short drive away from Seattle.