1- Facebook is more a social networking site where you can make friends often based on social interest . It allows you to post pictures as well. On the other hand, Twitter is more a micro blogging site allowing its users to post short messages (140 characters long) .
2- Facebook allows you to create pages for brands,business,social interest etc. while Twitter does not provide any feature of creating pages.
3- Facebook status updates remain active for a much longer period of time when compared to the Twitter updates. Tweets remain active for a short period of time.
4- Twitter allows you to find tweets based on certain topics with the help of # tag. Facebook does not have any such feature of tracking conversations.
5- Facebook allows you to create groups where you can send bulk invites to people whereas Twitter does not have any facility to create groups and to send bulk invites.
6- Facebook has a much larger user database than Twitter.