...but one will be better than the other based on your budget, preferences for customization, and hair needs.
Function of Beauty's hair quiz isn't as in-depth, but the customizable features (name, color, fragrance) make it feel more personal. It's also simultaneously flexible and inflexible: you can only buy its shampoo and conditioner in pre-arranged sets, but there are multiple sizes and combinations to choose from. Its products are cheaper than Prose's and are a great gift option.
What Prose lacks in camera-ready packaging it makes up for in its use of detailed data to create your unique formulation. Its products are more expensive, though it does have the added hair mask option, and you aren't constrained to pre-made bundles. If you're willing to spend a little more and don't care that it's not (yet) giftable, try Prose.
Thankfully, with whichever one you choose, you can enjoy high quality ingredients, great customer service, and the convenience of customized hair-care delivered right to your door.
Get your personalized hair-care formula at Function of Beauty here
Get your personalized hair-care formula at Prose here