The main point of the web audio api is for procedural generation of sounds rather than playing of pre-computed buffers or files. This is why "new Audio('effect.wav')" isn't a real alternative to it.
More to the point: As soon as you want to mix audio levels, <audio> alone is completely insufficient. You need mix control in order to fade background music and loops. I consider this a basic need; the Mozilla API allows you to roll something yourself, but Web Audio is more clearly suited to the application.
Mozilla had procedural audio generation through <audio> with a simple, documented API back when Chrome couldn't even play non-procedural audio through <audio> properly.
Simple, documented, and slower - you had to do everything in JavaScript. Web Audio API retains the ability to use JavaScript but provides a nice set of fast primitives.