I think any of the approaches could work, though I personally would much prefer #3 or #2 to #1. Switching off every scene makes it very hard to develop any sort of momentum within the session, and also encourages very linear, separate scenes -- there's much less room for cutting between simultaneous scenes, etc. If it was like a first half, break, second half set-up, that would be more manageable, but still seems awkward and fiddly to me.
Of course, #1 works better if you instead just run the game as mostly MCless, so that neither or both of you are just always MCing to greater or lesser degrees depending on what is happening. (I played a playtest of a game just last week that explicitly removed the single-MC role from the AW engine, and delegates MC-esque responsibilities based on a division of Fronts, basically.)
#3 would definitely be my personal choice, especially if everyone can figure out how to keep the campaigns short -- like 6-10 sessions or so -- so that the switching-off-but-staying-in-the-same-Apocalypse feels relevant, and whoever is MCing second still has plenty of room to add their fresh take on the material. Every other session could be excellent too, though, especially if the MCs figure out some ways to make that fictionally or thematically coherent. (By dividing Fronts, for example, or by having a setting that is split in some interesting way.) I think #2 is the best option if you have very compatible MCing styles and also really want to heavily riff on each others' contributions.