Which is better for windows? pthreads or CreateMutex?
One thing you need to keep in mind is what is the future of this code. Do you plan on developing (and releasing) on both platforms in the future? Or is this a one way port?
The best thing to do when porting a project is to keep the actual changes to the code as minimal as possible. In your case, this would mean going with a pthread solution. That being said, if you are planning this to be a one way port, going native never hurts. :)
I would take some time to fully examine both stratigies and then implement the one you feel most comfortable with.