Safest is to do both! The saving you really need to do while paying down credit cards is to build your emergency fund, which is six months of expenses in a readily accessible account. Building that, and replenishing it when you use it, will give you the cushion to ensure you don’t have to borrow heavily on credit cards in the future. We recommend that you split your savings 50/50 between credit card payments and building your emergency fund. When it reaches six months of expenses, feel free to put 100% to those credit cards until they are paid off. After that, you can get back to saving — most likely to max out retirement accounts.
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