Freezing potato soup
you can freeze both. the potatoes tend to get grainy but like the other poster said, you can puree it with an immersion blender to smooth it out. adding the cream after it's been thawed won't really help with the graininess of the potatoes. if you are using a roux method to thicken it won't thaw grainy. if you let the soup cool completely before you freeze it, you typically won't get the graininess. at least, i never have. i make butternut squash bisque all the time and never have any kind of issue after freezing. it's starch content is less than that of potatoes, so it thaws beautifully.
I don't think you can freeze potato soup and expect the same level of creaminess after defrosting. I've tried it. The result are still tasty, but the consistencies is somewhat grainy. You can try a stick blender to smooth it out and add more cream.
I'm not sure about butternut, but I want to say it would work better than potato.