Join us = Come and enjoy our company.
Join with us = Come and be like us.
"Join us" is most common for invitations. But "join us" can sound like an imperative. So people often change it to "Please join us" and they also use this "Join with us" which has the feeling of being more inclusive and "softer" It is often used around Christmas by churches.
"Please join with us in celebrating the birth of Jesus". It implies that there is an existing group that is definitely attending the event (in this case the regular church -goers) and also that anyone else is welcome. So you don't have to join the church to attend Xmas, you can just go to the Xmas Day ceremony and enjoy the celebration.
