This battle is over your standard black cup of joe that you need right now.
McDonalds may have the largest budget for marketing so anyone that owns a TV probably see's the ad that shows McDs coffee is $1 all day, any day. This of course is a draw and they want you to buy a $3 breakfast sandwhich at the same time. Don't kid yourself McDs isn't loosing any money selling the cup of black gold for only a dollar. It's down to a science and they make a profit on every item they sell. 
Lets now talk about the competition and why I decided to have this battle. If I'm going to have a breakfast sandwhich (which I do when travelling for work) I prefer Burger King (BK) over McDonalds. Theres two primary reason but this isn't about the sandwhich it's about the coffee. So my most pleasent surprise was when I stopped in and picked up a cup of coffee last week was the price! Fifty cents; What? are you kidding me, 1/2 the price of McDonalds this harkins back to the days of when you could buy your coffee our of a machine that dispensed the paper cup with a bonus game of poker on it for a potentially free cup of coffee.
So how makes the better cup of coffee? I'm not sure I care, I consume more coffee that water so for me it's about the economics of it as long as I can stomach it.
Do you have a preference? Let me know in the comments down below.