What is the need for invite only channels when personal channels works the same?  

Personal channels are accessible only to users added in the channel i.e. they are also closed channels. But Invite only channels differs from that of personal channels by their classification — Official.

Without Invite only channels, all official topics and discussions between closed group of users will have to be classified under Personal. Therefore to help users retain a channel's purpose and categorization, invite only channels are provided under Organization and Team.