The Gecko API is very basic, it just gives you access to sample buffers in Javascript, so everything must be processed in Javascript.
The Web Audio API is a much more fleshed out API, built on the higher level audio APIs used in professional sound apps. You can use it to process raw buffers, but you can also use it sequence and compose many effects on audio buffers with very low latency timing requirements without having to write time critical javascript DSP code and hope for the best that no delays or scheduling skew creep in.