Separate. I never take more than a small underseat carryon filled with all the black clothes it will hold, and 2 pr squashy shoes. And a messinger-type bag with computer and cosmetics, just in case they insist on checking in my carryon. He needs an entire rollerbag for his running shoes. Another for water and energy bars. And yes, we are going to the same place

Have never lost a carryon, but rarely travel anywhere that you can't buy underwear and clothes when you get there.