So I have a very good story to use as an anecdote but I’m not sure whether I should save it for the free-topic yale essay or rather use it on the basic common app prompts.
What’s more important for someone who wants to get into Yale? Does the admissions committee put more emphasis on the Yale essay or the Personal Statement of Common App?
Thanks! 
@commonapplicant, more experienced hands might arrive with better informed opinions, but if it were me, everything else equal, I’d use it on the common app. I don’t think Yale AOs weight the Yale essay higher than the common app one.
Are you applying SCEA? In that case, you could make the Yale essay the stronger one (i.e., use the strong anecdote there), and then, if necessary, use it for the common app after the SCEA round. If memory serves, you’re allowed a couple of essay rewrites, but please verify that for yourself.
Thanks!
Yes, I’m planning to apply SCEA.
Are you really allowed to change the personal statement after you submit it to one school? I thought the common app freezes, and you can only work on your supplements.
I doubt that Yale AOs value one over the other. There is a reason why Yale chooses to have a supplemental essay - they want to hear directly from the student, and an additional Yale specific essay is a good way to do this. I suspect that most AOs read the common app essay before they read the Yale supplement, since it is first in the order of the application, but each AO probably has their own methodology for reading. I know the AOs place a lot of value on the short takes and the “Why Yale” question - I went to an admission reflection session at Bulldog Days and heard this first hand. Basically, I think everything in the application is important and is given careful consideration.
I would consider the supplemental essay question that Yale is asking this year (are they out yet?) and see whether your essay topic works better for the common app essay or the Yale supplement. I think both essays are an opportunity to shed light on different aspects of who you are. My daughter used her strongest essay for the common app and used it for all of her applications, and wrote a decent second essay on a different topic/area of interest for Yale’s supplement. The Yale supplement was fairly high level -“please reflect on something you would like us to know about you that we might not learn from the rest of the application, or on something about which you would like to say more”; she was able to tweak her essay and use it for several other schools. She also had to write completely new essays for other schools based on their questions, and definitely got better at this throughout the fall. You will certainly use both essays in one form or another for your other applications, and as IxnayBob indicated, you can edit and adjust all aspects of your app for each and every college.
Use your best material for the Common App since it can have multiple uses.
That said, keep in mind that an anecdote is not going to dazzle someone into admitting you. What will work is to reflect on the anecdote and put it into the context of your life.
The Common Application has specific essay prompts, and students should think very carefully about ignoring the directions and doing their own thing. Does your anecdote fit into one of the prompts for the Common Application? http://www.commonapp.org/whats-appening/application-updates/common-application-announces-2016-2017-essay-prompts
If your topic and anecdote do not fit neatly into a prompt for the Common Application, then you should use it for Yale’s Supplemental essay.