My cousin faced a similar dilemma. Initially, she was stuck and could not decide which college to go to. Ultimately she made a decision after analyzing the pros and cons of both institutions. She told me that one has to be extremely sure about what one wants to pursue in order to make this decision.
You should go for any of both the IIMs if
You may go for Christ University if
One major advantage of going for IPM from any IIM is that they all offer an exit option after 3 years, so if you give CAT and you are unable to get enough score to get shortlisted by any IIM, then you are on the safer side. This is because you will have an MBA degree and that too from one of the most reputed B schools in the nation. Whereas this may not be possible if you go for BBA.
People might be concerned that both these IIMs are comparatively new. But depending on the predictions these are bound to flourish in the years to come.
The final decision is based on your own convenience and interests.