It's a subtle difference, yes. I think that in this context, DELIVER means you deliver something. Like a final product, like a good piece of work. For Levi's they deliver a solid product consistently ("the expected").
BRING refers to the attitude you bring as a company. For Levi's they bring forth new ideas, new choices and new styles ("the unexpected"). Yes, it is grammatically correct to say you deliver these things, but in their message, I think the word bring has a more intense feeling. Deliver sounds more routine to me in this context.
Hope that helps!