Maybe because English isn't my native language... ;)
example1: crontab task details here ... >/dev/null
This will redirect STDOUT to /dev/null but leave STDERR untouched.
example2: crontab task details here ... 2>&1 > /dev/null
This is the same as your first example2, it will redirect STDERR to the device/file where STDOUT is pointing to at the beginning of the cronjob (redirection of STDERR to STDOUT is processed first) and then it will redirect STDOUT to /dev/null (leaving STDERR untouched, or better: STDERR still points to the device/file where STDOUT was pointing to at the beginning of the cronjob).
So under normal circumstances both examples would produce the same redirections: STDOUT writes to /dev/null and STDERR onto the screen (not regarding situations where any of these handles were pointing to e.g. a file).
I hope this wasn't more confusing than my first post...