No, they cannot. You have to choose one or the other.
However, I think most GMs will allow rogues to choose either or.
When it comes to barbarians, as a GM I would make you choose either Unchained or normal, and the other is not available to you.
Many of the rage powers the normal barbarian gets are much stronger the "equivalent" powers that the unchained barbarian gets. And then there are a few (stance rage powers) that would be worth it to a core.
There's just too much overlap and too many things changed, I think it's easier to just keep them separate.
I believe Mark Seifter talked about it in a post he made.
That specifically Unchained Rage and Rage Powers were meant for the Unchained Barbarian only (only it was more general to say the the abilities of Unchained classes were designed only for them). Someone had specifically asked about clerics with access to the rage subdomain IIRC.
However, it is within a GM's power to extend it to anyone.