Hey randombetch (nice name btw)
From what I've read about position titles I don't think it matters. With titles I think there's a few things to really consider.
Your main concern should lie with prestige - what exactly does your title mean at your company? If it is a little known company the admissions officer may or may not know how senior you are and will go by years of work experience. Obviously if you're coming from an Investment Bank (Analyst, Associate, VP, ED, MD) or a big consulting company the admissions officers will know where you're at based on your title.
In your case I would consider Senior Business Analyst or Senior Analyst in a Business Division to be the same since regardless of your position you're performing business functions in a senior analyst role. Good luck with your application!
Kudos if I've helped you!