Why is it one versus the other? Going to the dentist beats lots of even-less-pleasant things...

The Venture card lets you pay $59 a year to get 2% back good toward "travel" (whatever that means to them). Schwab or Fidelity will let you earn 2% back in cash, good for use on travel or anything else, for no fee.

With the checking account, if you hit their maximums by paying bills and writing checks, you would make 150 "miles" a month, worth $1.50 or less, subject to their restrictions on how you use them. You could earn a few cents more by using your debit card, but there wouldn't be much sense in that; if you do like making debit card purchases, you could get a rewards checking account instead. In any case, that might beat whatever you can earn in interest somewhere else, but I don't think I'd switch banks to earn that much.