Fit is very important. What did your gut tell you after you visited each school? If you want Greek life, go to Duke. If you want a school that has big time sports victories, go to Duke. Rice has residential colleges as opposed to Greek life and does not excel at major sports, particularly football and basketball.
If you think you could be happy at either school, then look at the numbers. If you want to up your chances to get in Duke, you should ED to Duke. Duke takes a higher percentage of its class ED than Rice does. Duke is very yield conscious. If you are a legacy at Duke, the legacy card is most valuable in the ED round. You can hedge your bets by going ED Duke and RD at Rice. https://today.duke.edu/2017/12/duke-accepts-875-early-decision-applicants
The principal question to ask yourself is If you get in Duke ED would you happily attend and could your parents comfortably afford to pay whatever the price is.