You'll probably want to boost Latios's Special Attack, seeing as A: that's his strongest stat, and B: the strategy involving him seems to call for a lot of firepower in that department. Go with a Modest nature and see what happens. Use Recover if you need to after boosting Latios's bite with Calm Mind. Timid is a recommended nature to try as well, considering the fact that Latios has an abundance of S Attack (especially with Soul Dew equipped) but not quite as much Speed.
For Latias, go with Modest either way. See above, even if her best stat isn't S Attack. In fact, given the standard movesets and strategies, you'll probably want that boost anyway.