I tried both programs when I took Music 101 at my university last semester (music theory for non-Music majors). I am not a professional musician, and I do not intend to have any future in music whatsoever. I spent about 4 hours with each program (Sibelius and Finale) and personally preferred the workflow and feel of Sibelius. I had not used either package previously, so I was basically a clean slate. I used Finale first, between the two, over the course of two days.

I liken my preference to Sibelius to my preference of Keynote over PowerPoint: it does everything I need it to do, but it looks better and it allows me to work faster with a better end result. I'm sure there are features of Finale that I didn't notice that were not present in Sibelius. I would argue that my presentations are light-years ahead of the simple pieces I put together with the notation software I tried. With my very limited experience, though, I would have to say that Sibelius is what I would choose to use should I ever delve into music again.