Every latest version of Pega product is backward compatible with exception from legacy or deprecated versions such as PRPC4.x.
The designer can import the RAP or product jar of older versions in the latest product release. Though, moving forward from Pega 7.3x provides lot of enhancement in the UI supporting latest HTML5 and CSS3 with enhanced and optimise code as compare to an older version.
Also, Flexi-box is introduced which is latest HTML component to support responsiveness to the higher extent.
Pega 7.3x has other enhanced feature as the template as well. So, all these features automatically leverage for your older application. And if you face any OOTB product issues after the upgrade which was working as expected, please raise a support request ticket with GCS (https://msp.pega.com).
I would suggest you to perform the upgrade from 7.1.8 to 7.3.1 so that all the rules and data will be upgraded from 7.1.8 to 7.3.1 version during this process and you don't need to be worried about the compatibility issues rather than installing 7.3.1 then moving your code from lower to higher version.