Burger Fi is pretty darn good. The onion rings are a key differentiator between Shake Shack/Five Guys. The rings, and the sauces too.
I think Burger Fi has a bit more variety too on their toppings. They also have a "secret menu" (yes, even more than the "secret menu" that is now on the app), so do your research before you start warming up your lips. I usually get the fries "limp", I am fine with "crispy" for smaller fries (McDonald's, Steak & Shake), but for a larger fry I like less crispiness.
And with all due respect to the Shack, Burger Fi comes CLOSE on shakes. A close second-place.