Additionally, the WebCrypto operations are built into the browser platform and cannot be overwritten by userland javascript, though the interface can be spoofed in browsers that do not support it natively.
I'm not sure it matters that WebCrypto is native and "can't be overwritten", given that all the glue connecting the crypto is pure Javascript and can easily be rewritten.
I'd be interested in reading about how SJCL's interface is cryptographically superior. Superior/inferior seem to have a particular definition in this context, and I'm not sure I understand exactly what you mean. I know you're an expert in the field and would love some more context on how I should be cautious with WebCrypto.
(Edited for clarity.)
(I wrote the document you're citing, for what it's worth).
FWIW, WebCrypto should only be available in a secure context (https://lists.w3.org/Archives/Public/public-webcrypto/2016Se...), though I believe only Chrome enforces that requirement at the moment.
I'd personally rather see browsers ship libsodium.js (or equivalent) than WC or SJCL.