oooooo... This is a tricky question and got me flamed sometime ago!
You see, Jessica, both are equally good. In fact there's also this little software: http://musescore.org/
(MuseScore) which is free and the exhibits of the resulting output are quite lovely, especially for one who doesn't need a professional output!
Now, I will repeat that both Sibelius and Finale are equally good in what they do. I used to be a Finale user since the late 90s and recently I started using Sibelius as well (for professional reasons), and I did realize that there were very very few things that the one software could do better than the other. It's mostly that they do things differently.
Personally, I'm not so fond of the music font Sibelius uses, but what the heck did I expect after one decade and a half of using Finale?!?!
HOWEVER, you should note that Sibelius has been in trouble recently: Avid (the mother company) fired ALL the UK based staff (which contained people working there for 15 years with huge experience, etc) and thus the future of Sibelius is nothing short of... uncertain. On the other hand Finale seems to also be in financial trouble. Shareholders are not happy and while traditionally coming out with a new version every year, suddenly this year they just skipped this process... And all this while MakeMusic (the company which makes Finale) bought Garritan (the company that makes sounds).
In other words, I'd say that for a budding composer the very best idea one could do would be to try out MuseScore and if he exceeds it's limitations then by all means move on to the next higher package. Until then I have a feeling that the inside quarrels, problems, nagging shareholders, etc will have cleared their place...