All of the paton's yarn I have used are NOT machine washable, they may have one that is, but I haven't used it so I can't help there.
Barnet Satin is dreamy soft! I LOVE it! In fact on of the premiee blankets I have right now I'm using it. It comes in worsted weight too and I've used both.
I have not used Bernat Softee Baby, so I can't compare it that way.