Just some thoughts on this:
In principle, I agree with Meaningful Username that we should make our decision irrespective of potential implementation difficulties, unless of course SE comes back and definitively says what they can and can't do for us.
Not having done any research, I was skeptical that Lilypond integration was possible, but it turns out MediaWiki have supported it with the Score extension since April 2013. That's a proof of concept, at least, but there may be other concerns for implementation on SE. Wikipedia doesn't render markup in-browser, for example -- though that problem has been tackled elsewhere.
One great feature of the score extension is that it supports BOTH LilyPond and ABC notation. Not saying we necessarily should have that flexibility here, but it's something to consider.
Some other things to consider:
- Does the syntax for either language present a steep learning curve? Discounting, of course, syntax that represents features not present in the other language.
- Do we need to make a judgement about quality vs. ease of implementation? Would it be better to have something quick and dirty, but to have it NOW; or to wait for an objectively better option to go through the slow cooker and come out done right, but LATER? I don't think SE is likely to agree to implement one parser now and then another down the line. The implications of such a transition are also worrisome.
Personally, I have very little interest in ABC notation when compared with Lilypond. Lilypond effectively has feature parity with professional engraving programs like Sibelius and Finale, and in many cases outputs notation that is prettier than all of them. I can't speak to the syntax differences and difficulties within the overlapping features, but I can say that the more complete capabilities of Lilypond are a big incentive to me to learn it fully, should it be the one we decide to implement.