Most of the application team I lead is in Brazil and the global IT leadership (US-based) now wants to move some of that work to a new global delivery center in India to be more cost effective, but I have doubts. The Brazil team is delivering good quality — is cost efficiency enough reason to relocate the work? What are the biggest pros/cons we need to consider?

In my opinion, I don't think Indian delivery center will bring significant cost savings compare to Brazil, but I am sure your organization would have done their cost-benefit analysis before making a decision.

From the question, you seem to imply that India delivery team might not delivery good quality compare to Brazil. Just curious, what makes you think that? while most known names of IT industry get their software products developed in India.

Yes, Cost is main driver value to reallocate, and YES it would bring challenges, the best way to use more automation and process driven approach in any task or activity required, teach them about the process and ensure you do not have people or resource driven approach ensure that process drive any task to be able to replace any resource anytime required

Besides the obvious cultura, comms and time zone differences, look at how deep the business knowledge of the Brazilian team is - transferring this will take very long to reach the same delivery levels. Also don't underestimate the increased management overhead required (specifically for remote teams in India) - you have to have VERY clear processes, defined deliverables, and disciplined communication are essential to maintain alignment and accountability.

Communications, and approach to quality and service. In any new delivery center you’ll experience a significant learning curve, and it will take time to be productive, and even longer to prove more effective.

You may need to add other criteria to the discussion (other than cost, but ultimately translate to operational costs), such as speed to value (is time zone difference an issue?), knowledge of the business (how long before the India team is up to speed?). Also, what will be the cost of transferring the work to India? Finally, if they still want to proceed, you can always try a pilot to validate your leadership team's assumptions...