Traditional portrait painting is usually done with oils and several parts are painted with a glazing technique, then the final details are applied thicker.
Personally, I like thick acrylics, the heavy body kind, for pretty much every painting technique.
You can make glazes by thinning them with water or acrylic medium and make them more transparent that way. It helps to know which hues are opaque and which are more transparent from the start - this info is usually on the tube.
Oil paint is pretty thick right out of the tube, so I feel like if you are trying to emulate the results of oils using acrylics, you should use thicker acrylic, at least that's my take on it.