With two teams, we should allow ourselves to have the option of writing the 'big' stuff with one, and the 'smaller' stuff with the other. Having two teams handle only the smaller level stuff, or, only the bigger threats would simply be redundant, and antithetical with the reasoning behind creating two seperate teams.
This does not mean, however, we are required to only do one type of story with each. But, we should take into consideration the reality of the teams right now, and the characters that compromise each.
With Grissom, Phil, Brianna, BF, RoboSquirrel, and Tiberius making up the total of VI right now, they aren't exactly what I would call a powerhouse line-up. The level of ability and power combined isn't enough to handle the cosmic, higher level threats right now. For them to become the world's protectorate, they would need some serious additions to their line-up. More power.
Right now, VE remains at an even level of power, even though they have more members. Drake, Gaunt, Adem, Lykopis, Icarus, Ozzy, Tommy, and Victor. Only really Gaunt comes close to being a bigger-threat character. So, while they are able to deal with more exotic threats, they would still be hard-pressed to turn the tide during an alien invasion, or some other higher-level threat.
Therefore, the conclusion I have come to is simple. Each team handles their own brands of threats or adventurers in the way that's logical and believable, given their current levels of power. That means, if an alien invasion or some other cosmic threat popped up, it would more than likely take the combination of both teams working in unity as that 'Authority'-leveled team that some want achieved.
If the big threats are truly that...big....then, it's not like they'll happen every single story. So, then, everyone is happy. We do small stuff, and the writers who enjoy small stuff get their day. And, when we do big stuff, we bring the needed characters together, and do the big stuff, thus satisfying the needs of the more epic of us (which counts me).
Now, this does not prelude people creating new characters for VI, in place of the ones they are using now. If VI becomes more powerful, then, it would almost be a shame not to have them become Earth's defense force. But, really, only then.