You certainly cannot do both in a week, and that late in the season, I would opt for Dubrovnik. Even then, working in more than just Dubrovnik may be a stretch, only because travel between areas can be time consuming.
I would suggest getting a place in Dubrovnik as a base for the week. From there, there is plenty to do in Dubrovnik, plus many day trips or overnights. These would include:
Touring Montenegro
Overnight trip to Mostar
Visiting Ston
Overnight trip to Korcula
Wine trip to the Peljesac peninsula
Trip out to Mljet National Park
While all of the above seems like alot, having a base adds a great deal of stability, and you can pick and choose as you like.