Call of Duty will not be getting any exclusive content on Xbox, according to Phil Spencer. Instead, it's expected that no matter what platform you play on, there will be 100% parity.
On the official Xbox podcast (clipped by CharlieIntel), Spencer says that Xbox has "no goal of somehow using Call of Duty to get you to buy an Xbox console." He also confirmed that there will no longer be different betas depending on the platform you're playing on for Call of Duty.
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This does sound a little too good to be true right now, and there is a chance that this could change in time, but as of right now it does seem like Xbox is being rather cautious with how it manages its big new purchase. Immediately making changes to Call of Duty would likely put a fair few warning sirens in people's minds, so the safest bet does seem to be to keep parity going, at least for now.