You have my sincerest condolences!
Kidding aside, a brand switch would mean a complete card reissuance and deactivation of the old BIN. You have the upfront cost of the reissue, which will be substantial with EMV cards. You don't necessarily have to do a mass reissue with your EMV strategy. If you stayed with the same brand and BINs you have the option of reissuing EMV cards at standard reissue and spread out the cost over time.
Although we didn't switch Brands, I have done complete BIN conversions twice in my career. They are a lot of work, and no matter what efforts you make to communicate with your customers, it will cause cardholder disruption and inconvenience. Not only will your customers have new account numbers and different card benefits because of the brand shift, they will be dealing with learning how to use an EMV card. The residual activity on the old BIN also takes a long time to wrap up; we called it the gift that keeps on giving. Just when you thought you were about done...
Bottom line, make sure the benefits of switching brands (lower costs, better enhancements, etc...) outweigh the negatives.
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Let's start at the very beginning; A very good place to start...