Not a perl solution, but may be good for you if you're on Linux:

find BIG_1 -type f -exec touch \{\} \;

cp -au BIG_2/* BIG_1/

This will update the modification time of all files in BIG_1 and than copy all files from BIG_2 which don't exist in BIG_1 to there (-u means update: copy only files which have no newer file of the same name at the target).