Don't forget that all credit card offers aren't available to everyone. If someone says they have a Prime + 1% from XYZ Bank, that doesn't mean you can get it too. Your past credit history is a factor. So is theirs.
The longer I go without carrying a balance, the better the offers I get. Yesterday I got an offer from Discover for 0% interest for 18 months. I don't care, because I refuse to carry a balance. Yes, it's good to shop around, but sometimes you take what you can get.
And since they all have the right to change the rate at any time, what they might give you this month might be taken away next month. I know of card issuers that offer a "fixed 7.99% APR" -- until you start racking up a balance, then they jack the rate up to 18%. Yeah, it's legal. You have the right to move your balance somewhere else, but they are hoping you can't get another card.
The point is don't lose sleep over tiny differences in APR. If you pay in full every month, it won't even matter.