I am a fan of The Points Guy blog and webiste, which are free to access. Here is a recent article about price differences for booking flights with the airlines or via a credit card portal.
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Atlanta, GA, USA
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The other thing this article does not mention is that if you book through one of these websites that website is now your travel agent. So when you need to change the flight or there is a flight schedule change that doesn’t work inin most cases, you’re going to have to call Chase, Citi, AMEX and deal with them.
I’ve learned that it’s best not to put a third-party in between me and the airlines.