Salem

So when sleeping in a bed my avatar is still there.

But if I log off by the old method does my avatar vanish making him safe?

Well, safety is currently equally the same no matter how you log out, someone can't hurt someone that sleeps in a bed even if they destroy the bed. This may change though.

Either way you log out you can still be summoned and killed if you have left criminal scents, and you can still be robbed blind if someone gets access to your lean-to.

Your character's life is safe logged out unless you do crimes. Doesn't matter the method, bed is safe as of now.
Your stuff isn't safe, that's why you build a personal claim, walls and torchposts and braziers.