It depends. I use both every day. I believe each brings its own set of tools and the choice depends on what needs to be done, or of course, your publisher requires one or the other as mine does. So what is the difference? I'll attempt to briefly summarize the strengths of each, and what I use each to do.
Finale
There's little doubt Finale is the industry standard platform, the Adobe Photoshop of notation software, an application that allows the user endless opportunity to customize and adjust settings on the most granular level. This is Finale’s biggest strength, in my opinion. Just about anything can be tweaked, swapped, customized, to a level of precision the Sibelius cannot match. This level of control is of course, why publisher and engravers favor Finale. When I engrave, I want to know exact sizes, distances, and values, down to the point or even EVPU (Enigma Virtual Page Unit—a tiny unit of measure within Finale, 288 EVPU = 1 inch). Expressions, note spacings, lyric baselines, slur settings—really just about every component of your music can be adjusted down to the EVPU in a dialog box, which is a pretty powerful level of control and consistency. Rulers and guides can be drawn onto the page to assist in alignment. Of course, as in pro-level apps like Photoshop, this level of control and precision comes at a cost to the beginning user. The software can be tough to get around in, to find basic things, or make your music look decent right out of the box, but in capable hands, can be magic.
Sibelius
The Finn brothers and Daniel Spreadbury have done a phenomenal job of making this notation app as simple to get around in, and compose as a word processor. Sibelius is unmatched in its user interface and overall experience. Methods and keystrokes are intuitive and easy to remember and editing/adjusting objects is all about dragging. There are many back-end dialog boxes with more precise settings for objects and distances and whatnot, similar to Finale, but not quite as thorough. Sibelius operates on a principle of relative music size and spacing. Rather than absolute sizes and positions on the page, Sibelius favors objects to be relatively spaced according to the size of the music. This creates some anomalies and obstacles for an engraver. Sibelius lacks the ability to position an object with an X,Y value on the page. For example, positioning a text block in exactly the same spot across multiple documents is not possible. Positions are relative to the music, which of course, varies piece to piece. On the other hand, Sibelius’ automatic layout tools—automatically adjusting expressions and hairpins to be in line and fixing collisions—save me countless hours of manual adjustment. Add a dynamic and it’s immediately in line with others on the system. Add a hairpin and it is straight, perfect, and in line. With Sibelius, just about every staff object is intelligent, knowing its context and proximity to other objects, and when in conflict, moves itself out of the way—and adjusts other applicable objects within the system with it. It has also been my experience that Sibelius creates a better linked part layout on its first try, cutting down my part layout time by at least half.
The right tool
Typically I do my copy work in Sibelius. The speed of entry, editing, and relatively clean layouts all add up to tremendous time savings, which when preparing for a session, is time I’m already short on. Finale is an amazingly powerful and complex platform, and oftentimes the choice of publishers, and what I prefer to do my more precise engraving work with. Anyone looking for a future in publishing ought to invest the time and really learn Finale. Choose what is right for your project or client, and always look for ways to work more efficiently, while making your music beautiful.