What's your opinion of a re-applicant to Law School A mentioning in his/her application that he/she was admitted to but turned down Law School B last year. The purpose of this is to show Law School A how much the applicant wants to attend Law School A---so much so that he/she is willing to turn down Law School B and risk not having any law schools to attend just for a chance at getting into Law School A. Personally, I thought mentioning this might come off as a bit unprofessional. (A and B are similarly ranked and are both among the top of the T14. Neither of them ask for Why School X essays.)
The short answer: I wouldn't bother mentioning having turned down School B in your reapplication to School A.
That's not because I consider it unprofessional, but rather because School A most likely won't care that you turned down School B. If School A doesn't ask "Why Us?" in its application, it's likely (1) already assuming you really want to go there just by virtue of submitting an application or (2) doesn't care much about your motivations for wanting to go there (although probably does care about plenty of other things). They do, however, have to worry about yield protection (what percentage of their applicants accept their offers of admission), so they do care about the likelihood that you would accept their offer if they made one. Some schools have to care about that more than others, depending on how strong a brand they have.
So perhaps that's what you're getting at: Will it help ease their yield protection concerns if you tell them you were willing to turn down a peer school in order to reapply?
There are a number of ways you can demonstrate your interest that I think would work better. You can visit the school, you can apply binding Early Decision (if they offer that), and you can write an essay laying out the case for why you really want to go there.
Given that School A and School B are peer schools, the argument for preferring one over the other comes down to fit — how School A will do a great job helping someone with your background and goals get from Point A to Point B to Point C, and why it would be a great learning community for you to join. For schools that ask "Why Us?" in the essay, those are essential things to address. For schools that don't as "Why Us?", you don't have to write about that, but in your case you probably should, since you feel so strongly about School A. (I assume you didn't write them a "Why Us?" essay the last time around.)
The bottom line is that if you have important things to say on that subject this second time around, stay focused on School A. You don't need to contrast School A to a different school to make your case. I don't know what other schools you might be applying to this year, but if School A is the only one you're applying to, I would tell School A that it is the only one you want to invest in, and that you're not applying anywhere else.* Bonus: If School A offers binding Early Decision (something that maybe you wouldn't have taken advantage of before, but that you would consider now), that's also a put-your-money-where-your-mouth-is way to prove your love to a school.
*Can you get away with lying about that? Don't be tempted. Schools can find out pretty easily where else you've applied.
Anna Ivey is the former Dean of Admissions at the University of Chicago Law School and founder of Ivey Consulting. She and her team help college and graduate school applicants make smart decisions about their higher education and submit their best applications possible. Read more law school tips in The Ivey Guide to Law School Admissions.