Write a Business Case or Research?

Hey all,

One of my professors approached me with extraordinary opportunities (background - I am in my final year in undegrad at a relatively prestigious business school looking to apply to top deferred MBA programs) which are either to write a business case study (the ones you see at HBS, Darden) for the school or do academic research (possible to be published but will be extremely hard as top journals have >90% rejection rate). The prof told me that the case study will 100% be published under his guidance with some opportunity to be included in management casebooks/textbooks. 

Which one should I try doing? Is this going to be impressive to adcoms if they see that I was able to publish a business case? Of course, my intentions are not to do it for the sake of impressing the adcoms but I thought it would be nice to get some merit and recognition for my work.

I don't have a particularly strong profile in terms of GPA, but my GMAT, ECs seem to make up for my application. I am just honestly quite nervous about the process and feeling the stress as the senior year goes by.