Is it better to replace the homepage with the user profile after log in?

I'm working on a web application where I also need to code a user registration/login feature.

I'm in the process of working on the user-side of the system (in other words, what the user sees after the log in is done), and I was wondering, in terms of the URL of the user area, what is the better option, UX-wise:

  1. Redirect users to domain.com/feed where they can see their latest updates etc, and also access other users-only areas (for example domain.com/messages).
  2. Redirect users to the homepage, which will detect the user is currently logged on, and display the 'feed' (for example) as the homepage instead of the usual marketing front page displayed to visitors who haven't logged in yet. A few examples are facebook, trello, twitter...

I'm assuming the 'better' option would be the second one, since it allows the user to see what is most important (probably) to them faster, and without the need to enter a specific URL. With that being said, I have no UX experience/knowledge, and would like another input on the matter.