I think the strategy here is to individualize itself from McDonald's, which serves virtually the same food. By using the slogan "have it your way," I think Burger King is trying vaguely to seperate itself from fast food franchises.
However, I don't think it works for them. The slogan is too vague. McDonald's has "America's fries." What does Burger King have, besides from burgers (and those really good funnel cake stick thingys)? I think because Burger King is such a huge corporation, they are able to get away with vague advertising. However, in reality, there are alternate options that more people are gravitating to, such as Five Guys.
Burger King's advertising focuses on a wide audience, making the ads seem impersonal. There is no advertising geared towards kids saying, "Get this really cool toy in your Happy Meal!" I think if Burger King wanted to succeed, they would gear their ads towards a certain audience. "Have it your way" is a good start, but maybe they should focus on what we can have our way instead of just saying we can have it our way.
Now that I think about, "have it your way" might be a little suggestive if read the wrong way.