Should we be slicing stories vertically or horizontally? Does it even matter?

Should we organize the requirements in our user stories by architectural layers or by small units of functionality? 

Both approaches divide the work up into smaller batches, but what good are pieces of software if they're not actually usable? That's what happens when we slice stories horizontally (e.g. a user story to build a non-functional screen). 

Horizontal slicing brings on risks to the organization, like:

Vertical slicing, however, allows our teams to be agile by ensuring the delivery of functional, valuable capabilities driven by user needs and feedback