In the title of your post, you gave 2 different choices. However, the two sentences above are absolutely identical. I think you have answered your own question! It should read:
Keep in mind the BrE and AmE are sometimes very different when it comes to plural verbs. So in AmE, we would never say "family are..." In the example you gave, the AmE version would be "His family is full of perfectionists" or "His family is strictly perfectionist."