The reason to get new cards is to lower your total credit utilization. While the typical rule of thumb is no more than 33%, the optimal number is actually around 10%.
So, if you are using more than 10% of your limit on your other cards, it might help to get a new one.
That said, I have both an AmEx and Discover. They both have their different benefits, but I like the AmEx much better.
I have the Blue Cash AmEx. The 3% cash back on groceries and 2% on gas is really nice. I also like how each purchase I make with it is covered by a warranty from AmEx itself, so if I have a defective item and the merchant is being useless, I'm covered. It's also extremely fun to have a transparent credit card.
The Discover card has 5% cash back on various categories at various times, but they tend to be for certain luxuries that I generally tend not to indulge in. As a result, it builds real slowly. Whenever I had to call them, they're also noticeably less professional than AmEx.
Generally speaking:
AmEx: better cash back for essentials, extra protection, high APR
Discover: better cash back for luxuries, low APR
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