Quote: "What could affect the quality of the sound?"
Imperfections (inductive and capacitive properties) of the various components driving the coil will have an influence. For example, a perfect square wave isn't possible to generate, you'll always have transition times and inductive spikes, as can be seen in this picture:
The other thing is what material you use for the spark gap and what shape you make it. It needs to be material that doesn't oxidize easily, and preferably each electrode should be be pointy. My prototype does none of that.
Quote: "Is this something that could outperform a typical speaker?"
For high sounds, yes. The big difference between conventional speakers and plasma speakers is conventional speakers have a certain mass. Because of this, they will also have a limit to how fast they can vibrate (I believe the tweeters have a limit of around 80 kHz). Plasma speakers on the other hand have no mass, and thus also have no upper frequency limit.
For low sounds, the mass becomes an advantage. Plasma speakers are unable to produce deep sounds (<80 Hz or so), so conventional speakers will certainly outperform a plasma speaker when it comes to deep sounds.
Quote: "Is the required power linear to that of a typical speaker in terms of loudness?"
The output loudness is linear when above a certain frequency threshold. As mentioned above, deep sounds are lost, so there's some form of a high-pass filter.
TheComet