SHOWING HOW YOUR LAW FIRM IS DIFFERENT

This is very similar to showing how one individual human being is different from another. Your law firm has the same lawyers, legal education, same market, same responses to legal problems. In essence it sounds just like a commodity situation so it is difficult to say that your pork barrels are better than the other chaps pork barrels .
But there is a fact in your favour already, you know that each person you meet is different somehow because he has a unique personality, way of thinking,of doing things of approaching problems, a special work ethic and so on and so forth.

The limits to which you can show how your law firm is different are really set by how much thought and effort you put into it.
Thus it is clear that those law firm that do more thinking come up with better approaches and service levels. They are always seeking to improve and if this is a character trait at your firm then you are already different from other law firms. You do it because you seek to be better and not to hang yourself as the poster child for a unique law firm.

Now while it is admittedly difficult, clearly demonstrating the ability to understand your clients problems is a certain way to show how you are different. This can be understood as firm wide empathy and it is something that will tilt the decision in your favour when the client is putting together her internal mix of factors to make her hiring decision.
You can also come up with an innovative solution and show how it is innovative or a world apart from what exists. This is where your long hours of dedicated study and thought will yield fruits as this is where ideas come to you that may not occur to others simply because they were not looking for them.

The singular theme to show you are different is to prepare differently, to put in hours of deep thought and study on the matter. No one can do this for your firm and you certainly cannot market an average product for a premium price.