Is there a way to robocopy using /MIR only those files from source, that are older X days then the files in destination?
/MINAGE:N should do the trick:
robocopy /? [...] /MINAGE:n :: MINimum file AGE - exclude files newer than n days/date.
This will of course take into account the difference from the current date and time, and not of the destination file, but if you run this script daily the result should be the same.