However, notice that they only claim that Lilypond's default output tends to be better than other software's. It's not always as good as a good manual engraving. You have to tweak it to get it right.
Just today I printed this Tchaikovsky piece. Compare the manual engraving with a Lilypond output here (1st and 3rd links):
In particular, look at the the Poco meno mosso section at pages 6 and 5, respectively. While the original has 2 bars in one line, the Lilypond version has 3. Not only the notes look too small, but the 8va in the second bar is almost unreadable.
I've mined Mutopia for the majority of music, but there are maybe 30 songs I've done by hand just because they were obvious holes in the selection. I'm a little unsure about offering CC-licensed stuff in the app, but my Etude-converted songs are also offered under CC and I'm going to be linking to the licenses, so I think it should be fine.
I'm going to try to write a post to show HN about the tech behind it. I wrote my own .ly parser/preprocessor in Python as part of the song conversion. To help the forked version of Lilypond correlate the screen position and time offset of notes in the piece, I ended up having it do things like unroll macros and loops and do all the layout changes I needed to make em work in the app.
As a nice bonus, Lilypond is also usable via a graphical interface, Denemo [1]. I've never used Sibelius or Finale so I can't comment on how they compare.
What I really wish were available, however, is the IMSLP catalog [2] in digital form (not PDF scans). Is there an app out there to OCR sheet music?
It's been a long time, but yeah. I just checked it out again. To my eye, the output does not look nearly as good -- it's basically on par with the music authoring software I was trying to use in the late 90s...which is not really that great. Sure it gets notes on a page, but is it readable?
To be fair, TeX is not really intended for musical notation, so it's cool they managed to get that kind of output. But Lilypond is really designed to produce beautiful, readable scores.
I remember, in a previous life as a violinist, that certain scores were just really hard to read, or not beautiful, it really killed my motivation to play them. Even familiar favorites, if engraved poorly were just no fun to read off of inferior pages.
Lilypond is nice, but its input language is (very powerful but) a bit clumsy and verbose. Others who feel the same way might want to take a look at PMW (http://www.quercite.com/pmw.html) which also produces high-quality PostScript output and has a more friendly syntax. Its author, Philip Hazel, is better known for the Exim mail transfer agent and the PCRE regexp library.
A program with such visual output could really benefit from a gallery page on its website. I found some examples of which it is capable of on http://lilypond.org/switch/tour
While I personally believe the GPL to be a poor license (in fact, I don't consider it to be pro-freedom in the least), criticizing others' license choices is just obnoxious. If you dislike it, don't use the software. If you really don't like it, compete with them.
That essay is a very nice rundown on the types of problems lilypond has dealt with in terms of working out how to create beautiful sheet music.