You can compare file modification times with test, using -nt (newer than) and -ot (older than) operators:
test
-nt
-ot
if [ "$file1" -ot "$file2" ]; then cp -f "$file2" "$file1"fi
Here is a POSIX solution:
find -name file2 -newer file1
Or even shorter and nicer, look at man stat:
man stat
stat -c %y file