Quick WebCrypto POC created a long time ago.
AES Benchmark comparison of asmcrypto.js (GCM, CBC) vs WebCrypto API (GCM).
Implementation is most likely not secure: !!DON'T USE FOR CONFIDENTIAL FILES!!
Results (Firefox 71.0 64-Bit; Arch-Linux; AMD FX-8350):
Webcrypto API: 775 ms
AsmCrypto (GCM): 4855 ms
AsmCrypto (CBC): 1950 ms