We'll see but I think we should keep games separated and only ask that someone who is an AP in one game must always behave like an AP (fair-play, friendship,...) in each and every game where AP is present, regardless of the faction he is playing there. In other words: no jerk, nowhere.
I feel like this because, when AP is in three games, we'll have a situation with 3 factions in AO, 2 in SWTOR, and 3 in TSW, so 3x2x3 = 18 possible combinations. It would be quite crazy to demand that everyone playing in AP in one game plays the same combination as the org AP in all games, so would have to pick 1 combination only on 18 available if he plays the three games!
That said, I would prefer AP's to be always together regarding factions but it's quite impossible (for example a Sith may discover us in TSW and join us... we can't ask him to drop Sith because we are Republic!)