Ohhhhhh, I love this question, because it gives me a chance to say, SIZE DOES MATTER! and it also gives me a chance to play! And by play, I mean, experiment, fiddle and futz and muck around. My Facebook page becomes hostage to these whims and this I enjoy.
Ok, diving in. As of today (January 15, 2018), the dimensions that work best for your Facebook Business page are:
How do I go about designing this?
If you want the best of both worlds and don't want to compromise your design, my advice is to size for mobile but design for desktop.
TIP: Keep your logo, page name or any other critical text outside of the "pink bands" as this is a no-go area for desktop view.
See it for yourself in action over on my business FB page.