I have both cards. They both get the 10% bonus. For both if you then qualify for Preferred Rewards you get that instead of the 10%. It doesn't stack--you start earning 25% instead of 10%.
The biggest differences is in the way you get your cash back. With the PR card you just get cash deposited into your bank account. With the TR you have to "redeem" travel points by ticking off things on your statement that counted as travel--but since it's defined so loosely, and includes everything from Uber to Parking to restaurants, there's always something there you can credit, and then you get cash back in your bank account, so it's basically cash back with a hoop you have to jump through.
The Premium Rewards card has an annual fee but it's easy to wipe that out: the $100 for airline incidentals (in flight food, entertainment, bag fees, etc.) is more than the annual fee by itself.
One thing to consider is pairing either of them with the BoA CashBack card with is a no-AF card. Especially if you were looking for dining, you could pick dining as your 3.3% category on cash back card and use travel at 1.6% for all else. It would only make sense to go to the premium card in that case if you were going to blow past the $2500/quarter limit on the 2% and 3% categories on the CashBack card. Also note you can get a co-branded Visa version of the CashBack card if, like me, you wanted to use it at Costco in the 2.2% category. Note these grow with preferred rewards too--it can be a 5.25% back on dining card and 3.5% back at Costco, at which point you might find you want two of them (the $2500/quarter thing starts to be a real limit for groceries+dining for me).
BoA does let you re-use a hard pull so if you apped the TR or PR card, you could follow up with an app for the cashback a few days later without getting hit with a second HP (but you do get a second new account, so it's not totally "free" to your credit score.)
