Finale now puts out a free program called Finale Reader, which works roughly the same way Adobe Reader works, except for with Finale files. You won't be able to edit them, but at least they can be opened up and printed. Although, having Finale NotePad was slightly better, but that's no longer free, apparently.
The simple way to think about the two programs is this:
Finale (intermediate to advanced): Finale is geared toward professional musicians and composers. It is built with publication in mind. It is very powerful in that regard. As of late, its begun to shift a lot more toward production, particularly with the availability of sample libraries. Unfortunately, it sacrifices some intuitiveness and requires a little more training or experience to really get the most out of it.
Sibelius (beginner to intermediate): Sibleius is user-friendly and makes a lot of the notion process simple and easy to use. However, it lacks many of the publication strengths that Finale is loaded with.
It's a lot like thinking of the differences between comparable Apple and PC computers. Sibelius is Apple. Finale is PC.