I own and use H.A. on my Mac. I'm looking forward to getting it working on GNU/Linux.
How it compares to Musescore? It is fair to say it is much more mature but also dated. H.A. in full includes tons of options, very easy access to MIDI details of the notes, every darn thing is editable. It also has a really remarkable "virtual singer" add-on. It also integrates audio recording, but minimally. H.A. has a very high quality plugin framework too. H.A. even does tab and imports GP files so it competes with Tux Guitar on that. Overall, it is a superb program that offers a lot over the current Musescore.
H.A. is not FLOSS, but they are exceptionally responsive to users, including an active forum and a whole procedure for involving users in development decisions. And they have a one-time-forever payment for the license.
Downside to H.A. is (1) it is non-standard and not open, so you can't as easily collaborate with anyone like you could with Musescore (though they do have a web-browser plugin and a shareware Melody Assistant program that can open full H.A. files, plus it does have lots of cross-platform export/import options). Downside (2) is that the interface is a bit clunky with lots of buttons and weirdness, feels very dated.
My feeling: Musescore, if it matures to where H.A. is now, will be far better because Musescore's style and manner of working is superior. But for now, H.A. offers a lot that Musescore is still just aiming for. I'd generally invest in using Musescore because it is FLOSS (but that's partly because I'm a music teacher and FLOSS makes things easiest for my students). H.A. is absolutely worth a try, and some features, like the virtual singer, may never exist in any other package...