Wasn't aware that you can have both, this is from OneMile...
Can you have both Hyatt Credit Cards?
You’re unfortunately only able to have one Hyatt Credit Card or the other. The application terms of the new
The World of Hyatt Credit Card state the following:
The product is not available to either (i) current Cardmembers of any Hyatt Credit Card, or (ii) previous Cardmembers of any Hyatt Credit Card who received a new Cardmember bonus within the last 24 months.
In other words, you’re not eligible to apply for the new World of Hyatt Credit Card if you currently have the old Hyatt Credit Card, and/or if you’ve received a new cardmember bonus on the old card in the past 24 months. You can, however, upgrade to the new card.