I like Dan's answer and believe that, as he says, both are common everyday words for educated people. Maybe he has not spoken the words this year but it is certain that he has read or heard them.
Personally, when I use "warrant", I use it as a synonym for "merit". When I say "that warrants my attention" I mean "that deserves (or merits) my attention)". That meaning is close, but not the same as, "justify".